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

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

( ((q => r) => (p => r)) => (((p => r) => s) => ((q => r) => s)) in TAUT A & (((q => r) => (p => r)) => (((p => r) => s) => ((q => r) => s))) => ((p => q) => (((p => r) => s) => ((q => r) => s))) in TAUT A ) by Lm1, Th1;

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

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

( ((q => r) => (p => r)) => (((p => r) => s) => ((q => r) => s)) in TAUT A & (((q => r) => (p => r)) => (((p => r) => s) => ((q => r) => s))) => ((p => q) => (((p => r) => s) => ((q => r) => s))) in TAUT A ) by Lm1, Th1;

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