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