let A be QC-alphabet ; for s being QC-formula of A
for x, y being bound_QC-variable of A holds
( not x in still_not-bound_in (Ex (x,y,s)) & not y in still_not-bound_in (Ex (x,y,s)) )
let s be QC-formula of A; for x, y being bound_QC-variable of A holds
( not x in still_not-bound_in (Ex (x,y,s)) & not y in still_not-bound_in (Ex (x,y,s)) )
let x, y be bound_QC-variable of A; ( not x in still_not-bound_in (Ex (x,y,s)) & not y in still_not-bound_in (Ex (x,y,s)) )
not y in still_not-bound_in (Ex (y,s))
by Th6;
then A1:
not y in still_not-bound_in (Ex (x,(Ex (y,s))))
by Th6;
not x in still_not-bound_in (Ex (x,(Ex (y,s))))
by Th6;
hence
( not x in still_not-bound_in (Ex (x,y,s)) & not y in still_not-bound_in (Ex (x,y,s)) )
by A1, QC_LANG2:14; verum