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

p 'or' q in TAUT A

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

assume A1: p in TAUT A ; :: thesis: p 'or' q in TAUT A

p => (p 'or' q) in TAUT A by Th3;

hence p 'or' q in TAUT A by A1, CQC_THE1:46; :: thesis: verum

p 'or' q in TAUT A

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

assume A1: p in TAUT A ; :: thesis: p 'or' q in TAUT A

p => (p 'or' q) in TAUT A by Th3;

hence p 'or' q in TAUT A by A1, CQC_THE1:46; :: thesis: verum