let A be QC-alphabet ; :: thesis: for p, q being Element of CQC-WFF A st p in TAUT A holds

(p => q) => q in TAUT A

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

assume A1: p in TAUT A ; :: thesis: (p => q) => q in TAUT A

p => ((p => q) => q) in TAUT A by Th7;

hence (p => q) => q in TAUT A by A1, CQC_THE1:46; :: thesis: verum

(p => q) => q in TAUT A

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

assume A1: p in TAUT A ; :: thesis: (p => q) => q in TAUT A

p => ((p => q) => q) in TAUT A by Th7;

hence (p => q) => q in TAUT A by A1, CQC_THE1:46; :: thesis: verum