let s be QC-formula; :: thesis: for x, y being bound_QC-variable 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; :: thesis: ( 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 ( not x in still_not-bound_in (Ex x,(Ex y,s)) & not y 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 QC_LANG2:20; :: thesis: verum