let A be QC-alphabet ; :: thesis: for x being bound_QC-variable of A
for p being Element of QC-WFF A holds
( bound_in (All (x,p)) = x & the_scope_of (All (x,p)) = p )
let x be bound_QC-variable of A; :: thesis: for p being Element of QC-WFF A holds
( bound_in (All (x,p)) = x & the_scope_of (All (x,p)) = p )
let p be Element of QC-WFF A; :: thesis: ( 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 Th6;
hence ( bound_in (All (x,p)) = x & the_scope_of (All (x,p)) = p ) by Th5; :: thesis: verum