let A be QC-alphabet ; :: thesis: for p, q, r being Element of CQC-WFF A st p => (q => r) is valid holds
(q '&' p) => r is valid
let p, q, r be Element of CQC-WFF A; :: thesis: ( p => (q => r) is valid implies (q '&' p) => r is valid )
assume p => (q => r) in TAUT A ; :: according to CQC_THE1:def 10 :: thesis: (q '&' p) => r is valid
then p => (q => r) is valid ;
then (p '&' q) => r is valid by Th1;
then A1: (p '&' q) => r in TAUT A ;
(q '&' p) => (p '&' q) in TAUT A by CQC_THE1:45;
hence (q '&' p) => r in TAUT A by A1, LUKASI_1:3; :: according to CQC_THE1:def 10 :: thesis: verum