\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t22\_zf\_fund1 (TMXxdXuXi1XFQqebXr6bgHvMyXVBWZfLtrY)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_classes2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_zf\_lang : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v8\_zf\_fund1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_zf\_fund1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_zf\_lang : {\iota}$ be given.
Let $ k8\_zf\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_zf\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_zf\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_zf\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_zf\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(\preoh v1\_xboole\_0~X2){\unicdbdjdcd}(((v8\_zf\_fund1~X1~X0){\unicdcdcdhd}(X2 \in X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_zf\_lang~X3){\unicdcdcdhd}(m2\_finseq\_1~X3~k5\_numbers)){\unicdbdjdcd}({\unicdcdadad} X4 .  (\\
m2\_subset\_1~X4~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}((k5\_zf\_fund1~X3~X2 \in X1){\unicdbdjdcd}\\
(k5\_zf\_fund1~(k8\_zf\_lang~X4~X3)~X2 \in X1)))))))\end{array}
\label{hyp:ehcdbdpfkhggpfggfhogegbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(\preoh v1\_xboole\_0~X2){\unicdbdjdcd}(((v8\_zf\_fund1~X1~X0){\unicdcdcdhd}(X2 \in X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_zf\_lang~X3){\unicdcdcdhd}(m2\_finseq\_1~X3~k5\_numbers)){\unicdbdjdcd}({\unicdcdadad} X4 .  (\\
(v1\_zf\_lang~X4){\unicdcdcdhd}(m2\_finseq\_1~X4~k5\_numbers)){\unicdbdjdcd}(((k5\_zf\_fund1~\\
X3~X2 \in X1){\unicdcdcdhd}(k5\_zf\_fund1~X4~X2 \in X1)){\unicdbdjdcd}(k5\_zf\_fund1~(k7\_zf\_lang~X3~\\
X4)~X2 \in X1)))))))\end{array}
\label{hyp:ehcdadpfkhggpfggfhogegbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(\preoh v1\_xboole\_0~X2){\unicdbdjdcd}(((v8\_zf\_fund1~X1~X0){\unicdcdcdhd}(X2 \in X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_zf\_lang~X3){\unicdcdcdhd}(m2\_finseq\_1~X3~k5\_numbers)){\unicdbdjdcd}((k5\_zf\_fund1~\\
X3~X2 \in X1){\unicdbdjdcd}(k5\_zf\_fund1~(k6\_zf\_lang~X3)~X2 \in X1))))))\end{array}
\label{hyp:ehbdjdpfkhggpfggfhogegbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(\preoh v1\_xboole\_0~X2){\unicdbdjdcd}(((v8\_zf\_fund1~X1~X0){\unicdcdcdhd}(X2 \in X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_subset\_1~X3~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_subset\_1~\\
X4~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}((k5\_zf\_fund1~(k4\_zf\_lang~X3~X4)~X2 \in \\
X1){\unicdcdcdhd}(k5\_zf\_fund1~(k5\_zf\_lang~X3~X4)~X2 \in X1)))))))\end{array}
\label{hyp:ehbdidpfkhggpfggfhogegbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}o .  (({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k5\_numbers~\\
k1\_zf\_lang){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}\\
((X0~(k4\_zf\_lang~X1~X2)){\unicdcdcdhd}(X0~(k5\_zf\_lang~X1~X2))))){\unicdcdcdhd}(({\unicdcdadad} X1 .  \\
((v1\_zf\_lang~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}((X0~X1){\unicdbdjdcd}(X0~(\\
k6\_zf\_lang~X1)))){\unicdcdcdhd}(({\unicdcdadad} X1 .  ((v1\_zf\_lang~X1){\unicdcdcdhd}(m2\_finseq\_1~\\
X1~k5\_numbers)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_zf\_lang~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~\\
k5\_numbers)){\unicdbdjdcd}(((X0~X1){\unicdcdcdhd}(X0~X2)){\unicdbdjdcd}(X0~(k7\_zf\_lang~X1~X2))))){\unicdcdcdhd}(\\
{\unicdcdadad} X1 .  ((v1\_zf\_lang~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m2\_subset\_1~X2~k5\_numbers~k1\_zf\_lang){\unicdbdjdcd}((X0~X1){\unicdbdjdcd}(X0~(k8\_zf\_lang~\\
X2~X1)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_zf\_lang~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}\\
(X0~X1))\end{array}
\label{hyp:dhbdpfkhggpfmgbgoghgbd}
\end{equation}
\begin{theorem}\label{thm:ehcdcdpfkhggpfggfhogegbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_zf\_lang~X3){\unicdcdcdhd}(m2\_finseq\_1~\\
X3~k5\_numbers)){\unicdbdjdcd}(((v8\_zf\_fund1~X1~X0){\unicdcdcdhd}(X2 \in X1)){\unicdbdjdcd}(k5\_zf\_fund1~\\
X3~X2 \in X1)))))\end{array}$$
\end{theorem}
\end{document}
