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

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

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

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

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

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

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