let A be QC-alphabet ; for p, q being Element of CQC-WFF A
for x being bound_QC-variable of A holds
( All (x,(p '&' q)) is valid iff (All (x,p)) '&' (All (x,q)) is valid )
let p, q be Element of CQC-WFF A; for x being bound_QC-variable of A holds
( All (x,(p '&' q)) is valid iff (All (x,p)) '&' (All (x,q)) is valid )
let x be bound_QC-variable of A; ( All (x,(p '&' q)) is valid iff (All (x,p)) '&' (All (x,q)) is valid )
(All (x,(p '&' q))) <=> ((All (x,p)) '&' (All (x,q))) is valid
by Th37;
hence
( All (x,(p '&' q)) is valid iff (All (x,p)) '&' (All (x,q)) is valid )
by Lm15; verum