let p be ZF-formula; for x being Variable holds
( bound_in (Ex (x,p)) = x & the_scope_of (Ex (x,p)) = p )
let x be Variable; ( bound_in (Ex (x,p)) = x & the_scope_of (Ex (x,p)) = p )
Ex (x,p) is existential
;
then
Ex (x,p) = Ex ((bound_in (Ex (x,p))),(the_scope_of (Ex (x,p))))
by ZF_LANG:45;
hence
( bound_in (Ex (x,p)) = x & the_scope_of (Ex (x,p)) = p )
by ZF_LANG:34; verum