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 holds

p => 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 implies p => r in TAUT A )

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

then (p => q) => (p => r) in TAUT A by Th19;

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

p => 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 implies p => r in TAUT A )

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

then (p => q) => (p => r) in TAUT A by Th19;

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