let A be QC-alphabet ; :: thesis: for p, q being Element of CQC-WFF A
for x being bound_QC-variable of A st not x in still_not-bound_in p holds
( p '&' (Ex (x,q)) is valid iff Ex (x,(p '&' q)) is valid )
let p, q be Element of CQC-WFF A; :: thesis: for x being bound_QC-variable of A 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 of A; :: 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 Th72;
hence ( p '&' (Ex (x,q)) is valid iff Ex (x,(p '&' q)) is valid ) by Lm15; :: thesis: verum