let p be ZF-formula; for x being Variable holds
( bound_in (All (x,p)) = x & the_scope_of (All (x,p)) = p )
let x be Variable; ( bound_in (All (x,p)) = x & the_scope_of (All (x,p)) = p )
All (x,p) is universal
;
then
All (x,p) = All ((bound_in (All (x,p))),(the_scope_of (All (x,p))))
by ZF_LANG:44;
hence
( bound_in (All (x,p)) = x & the_scope_of (All (x,p)) = p )
by ZF_LANG:3; verum