let p, q be Element of CQC-WFF ; :: thesis: for x being bound_QC-variable st All (x,(p <=> q)) is valid holds
(All (x,p)) <=> (All (x,q)) is valid
let x be bound_QC-variable; :: thesis: ( All (x,(p <=> q)) is valid implies (All (x,p)) <=> (All (x,q)) is valid )
assume A1: All (x,(p <=> q)) is valid ; :: thesis: (All (x,p)) <=> (All (x,q)) is valid
(All (x,(p <=> q))) => ((All (x,p)) <=> (All (x,q))) is valid by Th36;
hence (All (x,p)) <=> (All (x,q)) is valid by A1, CQC_THE1:65; :: thesis: verum