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 & p '&' (All (x,q)) is valid holds
All (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 & p '&' (All (x,q)) is valid holds
All (x,(p '&' q)) is valid
let x be bound_QC-variable of A; :: thesis: ( not x in still_not-bound_in p & p '&' (All (x,q)) is valid implies All (x,(p '&' q)) is valid )
assume that
A1: not x in still_not-bound_in p and
A2: p '&' (All (x,q)) is valid ; :: thesis: All (x,(p '&' q)) is valid
(p '&' (All (x,q))) => (All (x,(p '&' q))) is valid by A1, Th66;
hence All (x,(p '&' q)) is valid by A2, CQC_THE1:65; :: thesis: verum