let p, q be Element of CQC-WFF ; :: thesis: for x being bound_QC-variable 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; :: 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, Th70;
hence All x,(p '&' q) is valid by A2, CQC_THE1:104; :: thesis: verum