let p, q, r be Element of CQC-WFF ; :: thesis: ( p => q is valid & p => r is valid implies p => (q '&' r) is valid )
assume ( p => q in TAUT & p => r in TAUT ) ; :: according to CQC_THE1:def 10 :: thesis: p => (q '&' r) is valid
hence p => (q '&' r) in TAUT by PROCAL_1:52; :: according to CQC_THE1:def 10 :: thesis: verum