let p be ZF-formula; :: thesis: for x being Variable holds
( bound_in (Ex (x,p)) = x & the_scope_of (Ex (x,p)) = p )
let x be Variable; :: thesis: ( bound_in (Ex (x,p)) = x & the_scope_of (Ex (x,p)) = p )
Ex (x,p) is existential by ZF_LANG:22;
then Ex (x,p) = Ex ((bound_in (Ex (x,p))),(the_scope_of (Ex (x,p)))) by ZF_LANG:63;
hence ( bound_in (Ex (x,p)) = x & the_scope_of (Ex (x,p)) = p ) by ZF_LANG:51; :: thesis: verum