let p, q be Element of CQC-WFF ; :: thesis: for x being bound_QC-variable holds (All x,(p '&' q)) <=> ((All x,p) '&' (All x,q)) is valid
let x be bound_QC-variable; :: thesis: (All x,(p '&' q)) <=> ((All x,p) '&' (All x,q)) is valid
( (All x,(p '&' q)) => ((All x,p) '&' (All x,q)) is valid & ((All x,p) '&' (All x,q)) => (All x,(p '&' q)) is valid ) by Th40;
hence (All x,(p '&' q)) <=> ((All x,p) '&' (All x,q)) is valid by Lm14; :: thesis: verum