let x be bound_QC-variable; :: thesis: for p being QC-formula holds still_not-bound_in (All x,p) = (still_not-bound_in p) \ {x}
let p be QC-formula; :: thesis: still_not-bound_in (All x,p) = (still_not-bound_in p) \ {x}
set a = All x,p;
A1: All x,p is universal by QC_LANG1:def 20;
then ( the_scope_of (All x,p) = p & bound_in (All x,p) = x ) by QC_LANG1:def 26, QC_LANG1:def 27;
hence still_not-bound_in (All x,p) = (still_not-bound_in p) \ {x} by A1, Th15; :: thesis: verum