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

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

( q => (p => q) in TAUT A & (q => (p => q)) => (((p => q) => r) => (q => r)) in TAUT A ) by Th1, Th5;

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

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

( q => (p => q) in TAUT A & (q => (p => q)) => (((p => q) => r) => (q => r)) in TAUT A ) by Th1, Th5;

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