let A be QC-alphabet ; :: thesis: for p, q, r, t being Element of CQC-WFF A st p => q is valid & r => t is valid holds
(p '&' r) => (q '&' t) is valid
let p, q, r, t be Element of CQC-WFF A; :: thesis: ( p => q is valid & r => t is valid implies (p '&' r) => (q '&' t) is valid )
assume ( p => q in TAUT A & r => t in TAUT A ) ; :: according to CQC_THE1:def 10 :: thesis: (p '&' r) => (q '&' t) is valid
hence (p '&' r) => (q '&' t) in TAUT A by PROCAL_1:56; :: according to CQC_THE1:def 10 :: thesis: verum