let A be QC-alphabet ; :: thesis: for p, q, r being Element of CQC-WFF A holds ((p '&' q) => r) => (p => (q => r)) in TAUT A

let p, q, r be Element of CQC-WFF A; :: thesis: ((p '&' q) => r) => (p => (q => r)) in TAUT A

( p => ((q => (p '&' q)) => (((p '&' q) => r) => (q => r))) in TAUT A & p => (q => (p '&' q)) in TAUT A ) by Th28, LUKASI_1:1, LUKASI_1:13;

then A1: p => (((p '&' q) => r) => (q => r)) in TAUT A by LUKASI_1:20;

(p => (((p '&' q) => r) => (q => r))) => (((p '&' q) => r) => (p => (q => r))) in TAUT A by LUKASI_1:8;

hence ((p '&' q) => r) => (p => (q => r)) in TAUT A by A1, CQC_THE1:46; :: thesis: verum

let p, q, r be Element of CQC-WFF A; :: thesis: ((p '&' q) => r) => (p => (q => r)) in TAUT A

( p => ((q => (p '&' q)) => (((p '&' q) => r) => (q => r))) in TAUT A & p => (q => (p '&' q)) in TAUT A ) by Th28, LUKASI_1:1, LUKASI_1:13;

then A1: p => (((p '&' q) => r) => (q => r)) in TAUT A by LUKASI_1:20;

(p => (((p '&' q) => r) => (q => r))) => (((p '&' q) => r) => (p => (q => r))) in TAUT A by LUKASI_1:8;

hence ((p '&' q) => r) => (p => (q => r)) in TAUT A by A1, CQC_THE1:46; :: thesis: verum