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

p in TAUT A

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

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

then s => p in TAUT A by Th16;

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

p in TAUT A

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

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

then s => p in TAUT A by Th16;

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