let A be QC-alphabet ; :: thesis: for p, q, r being Element of CQC-WFF A st p => (q => r) is valid holds
(p '&' q) => r is valid
let p, q, r be Element of CQC-WFF A; :: thesis: ( p => (q => r) is valid implies (p '&' q) => r is valid )
A1: (p => (q => r)) => ((p '&' q) => r) in TAUT A by PROCAL_1:32;
assume p => (q => r) in TAUT A ; :: according to CQC_THE1:def 10 :: thesis: (p '&' q) => r is valid
hence (p '&' q) => r in TAUT A by A1, CQC_THE1:46; :: according to CQC_THE1:def 10 :: thesis: verum