let x be bound_QC-variable; :: thesis: for p being Element of QC-WFF holds
( bound_in (All (x,p)) = x & the_scope_of (All (x,p)) = p )
let p be Element of QC-WFF ; :: thesis: ( bound_in (All (x,p)) = x & the_scope_of (All (x,p)) = p )
All (x,p) is universal by QC_LANG1:def 19;
then All (x,p) = All ((bound_in (All (x,p))),(the_scope_of (All (x,p)))) by Th7;
hence ( bound_in (All (x,p)) = x & the_scope_of (All (x,p)) = p ) by Th6; :: thesis: verum