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

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

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

hence (((q => r) => (p => r)) => s) => ((p => q) => s) in TAUT A by Th2; :: thesis: verum

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

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

hence (((q => r) => (p => r)) => s) => ((p => q) => s) in TAUT A by Th2; :: thesis: verum