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_THE1:104; :: thesis: verum