let A be QC-alphabet ; :: thesis: for s being QC-formula of A
for x, y being bound_QC-variable of A holds
( not x in still_not-bound_in (All (x,y,s)) & not y in still_not-bound_in (All (x,y,s)) )
let s be QC-formula of A; :: thesis: for x, y being bound_QC-variable of A holds
( not x in still_not-bound_in (All (x,y,s)) & not y in still_not-bound_in (All (x,y,s)) )
let x, y be bound_QC-variable of A; :: thesis: ( not x in still_not-bound_in (All (x,y,s)) & not y in still_not-bound_in (All (x,y,s)) )
not y in still_not-bound_in (All (y,s)) by Th5;
then A1: not y in still_not-bound_in (All (x,(All (y,s)))) by Th5;
not x in still_not-bound_in (All (x,(All (y,s)))) by Th5;
hence ( not x in still_not-bound_in (All (x,y,s)) & not y in still_not-bound_in (All (x,y,s)) ) by A1, QC_LANG2:14; :: thesis: verum