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

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

( ((((q => r) => (s => r)) => (p => (s => r))) => ((s => q) => (p => (s => r)))) => ((p => (q => r)) => ((s => q) => (p => (s => r)))) in TAUT A & (((q => r) => (s => r)) => (p => (s => r))) => ((s => q) => (p => (s => r))) in TAUT A ) by Lm1;

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

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

( ((((q => r) => (s => r)) => (p => (s => r))) => ((s => q) => (p => (s => r)))) => ((p => (q => r)) => ((s => q) => (p => (s => r)))) in TAUT A & (((q => r) => (s => r)) => (p => (s => r))) => ((s => q) => (p => (s => r))) in TAUT A ) by Lm1;

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