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_1:31;
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