let A be QC-alphabet ; for p, q being Element of CQC-WFF A
for x being bound_QC-variable of A st All (x,(p <=> q)) is valid holds
(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 st All (x,(p <=> q)) is valid holds
(All (x,p)) <=> (All (x,q)) is valid
let x be bound_QC-variable of A; ( All (x,(p <=> q)) is valid implies (All (x,p)) <=> (All (x,q)) is valid )
assume A1:
All (x,(p <=> q)) is valid
; (All (x,p)) <=> (All (x,q)) is valid
(All (x,(p <=> q))) => ((All (x,p)) <=> (All (x,q))) is valid
by Th32;
hence
(All (x,p)) <=> (All (x,q)) is valid
by A1, CQC_THE1:65; verum