let p, q be Element of CQC-WFF ; :: thesis: for x being bound_QC-variable holds
( All x,(p '&' q) is valid iff (All x,p) '&' (All x,q) is valid )
let x be bound_QC-variable; :: 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 Th41;
hence ( All x,(p '&' q) is valid iff (All x,p) '&' (All x,q) is valid ) by Lm15; :: thesis: verum