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

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

( (p => q) => ((q => r) => (p => r)) in TAUT A & ((p => q) => ((q => r) => (p => r))) => ((q => r) => ((p => q) => (p => r))) in TAUT A ) by Th1, Th8;

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

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

( (p => q) => ((q => r) => (p => r)) in TAUT A & ((p => q) => ((q => r) => (p => r))) => ((q => r) => ((p => q) => (p => r))) in TAUT A ) by Th1, Th8;

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