let A be QC-alphabet ; :: thesis: for p, q, r being Element of CQC-WFF A st p => q is valid holds
(r '&' p) => (r '&' q) is valid
let p, q, r be Element of CQC-WFF A; :: thesis: ( p => q is valid implies (r '&' p) => (r '&' q) is valid )
assume p => q in TAUT A ; :: according to CQC_THE1:def 10 :: thesis: (r '&' p) => (r '&' q) is valid
hence (r '&' p) => (r '&' q) in TAUT A by PROCAL_1:50; :: according to CQC_THE1:def 10 :: thesis: verum