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

r in TAUT A

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

assume ( p => (q => r) in TAUT A & p => q in TAUT A ) ; :: thesis: ( not p in TAUT A or r in TAUT A )

then p => r in TAUT A by Th20;

hence ( not p in TAUT A or r in TAUT A ) by CQC_THE1:46; :: thesis: verum

r in TAUT A

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

assume ( p => (q => r) in TAUT A & p => q in TAUT A ) ; :: thesis: ( not p in TAUT A or r in TAUT A )

then p => r in TAUT A by Th20;

hence ( not p in TAUT A or r in TAUT A ) by CQC_THE1:46; :: thesis: verum