let A be QC-alphabet ; :: thesis: 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; :: thesis: 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; :: thesis: ( 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; :: thesis: verum