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 holds

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

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

then q => (s => p) in TAUT A by Th15;

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

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

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

then q => (s => p) in TAUT A by Th15;

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