:: Built-in Concepts
:: by Andrzej Trybulec
::
:: Received January 1, 1989
:: Copyright (c) 1990-2015 Association of Mizar Users


:: This article documents a part of the Mizar axiomatics - it shows how
:: the primitives of set theory are introduced in the Mizar Mathematical
:: Library.
:: Please note that the notions defined here are not subject to standard
:: verification, so the Mizar verifier and other utilities may report
:: errors when processing this article.
definition
mode object -> object ;
end;

definition
mode set -> object ;
end;

definition
let x, y be object ;
pred x = y;
reflexivity
errorfrm
;
symmetry
errorfrm
;
end;

notation
let x, y be object ;
antonym x <> y for x = y;
end;

definition
let x be object ;
let X be set ;
pred x in X;
end;