let p be ZF-formula; :: thesis: for x being Variable holds
( bound_in (All (x,p)) = x & the_scope_of (All (x,p)) = p )
let x be Variable; :: thesis: ( bound_in (All (x,p)) = x & the_scope_of (All (x,p)) = p )
All (x,p) is universal by ZF_LANG:16;
then All (x,p) = All ((bound_in (All (x,p))),(the_scope_of (All (x,p)))) by ZF_LANG:62;
hence ( bound_in (All (x,p)) = x & the_scope_of (All (x,p)) = p ) by ZF_LANG:12; :: thesis: verum