let p, q be Element of CQC-WFF ; :: thesis: for x being bound_QC-variable st not x in still_not-bound_in p holds
( p '&' (Ex x,q) is valid iff Ex x,(p '&' q) is valid )
let x be bound_QC-variable; :: thesis: ( not x in still_not-bound_in p implies ( p '&' (Ex x,q) is valid iff Ex x,(p '&' q) is valid ) )
assume not x in still_not-bound_in p ; :: thesis: ( p '&' (Ex x,q) is valid iff Ex x,(p '&' q) is valid )
then (p '&' (Ex x,q)) <=> (Ex x,(p '&' q)) is valid by Th76;
hence ( p '&' (Ex x,q) is valid iff Ex x,(p '&' q) is valid ) by Lm15; :: thesis: verum