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

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

( (q => s) => ((s => (p => (q => r))) => (p => (q => r))) in TAUT A & ((q => s) => ((s => (p => (q => r))) => (p => (q => r)))) => ((s => (p => (q => r))) => ((q => s) => (p => (q => r)))) in TAUT A ) by Lm21, Th8;

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

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

( (q => s) => ((s => (p => (q => r))) => (p => (q => r))) in TAUT A & ((q => s) => ((s => (p => (q => r))) => (p => (q => r)))) => ((s => (p => (q => r))) => ((q => s) => (p => (q => r)))) in TAUT A ) by Lm21, Th8;

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