%   ORIGINAL: 'h4/thm/bool/IMP_ANTISYM_AX_'
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Goal: !t1 t2. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
%   PROCESSED
% Assm ['HL_TRUTH']: T
% Assm ['HL_FALSITY']: ~F
% Assm ['HL_BOOL_CASES']: !t. (t <=> T) \/ (t <=> F)
% Assm ['HL_EXT']: !f g. (!x. happ f x = happ g x) ==> f = g
% Goal: !t1 t2. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
fof('HL_TRUTH', axiom, p(s(bool,'T'))).
fof('HL_FALSITY', axiom, ~ (p(s(bool,'F')))).
fof('HL_BOOL_CASES', axiom, ![T]: (s(bool,T) = s(bool,'T') | s(bool,T) = s(bool,'F'))).
fof('HL_EXT', axiom, ![V_3f31453,V_3f31449]: ![F, G]: (![X]: s(V_3f31449,happ(s(fun(V_3f31453,V_3f31449),F),s(V_3f31453,X))) = s(V_3f31449,happ(s(fun(V_3f31453,V_3f31449),G),s(V_3f31453,X))) => s(fun(V_3f31453,V_3f31449),F) = s(fun(V_3f31453,V_3f31449),G))).
fof('h4/thm/bool/IMP_ANTISYM_AX_', conjecture, ![T1, T2]: ((p(s(bool,T1)) => p(s(bool,T2))) => ((p(s(bool,T2)) => p(s(bool,T1))) => s(bool,T1) = s(bool,T2)))).
