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

p '&' q in TAUT A

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

assume that

A1: p in TAUT A and

A2: q in TAUT A ; :: thesis: p '&' q in TAUT A

p => (q => (p '&' q)) in TAUT A by Th28;

then q => (p '&' q) in TAUT A by A1, CQC_THE1:46;

hence p '&' q in TAUT A by A2, CQC_THE1:46; :: thesis: verum

p '&' q in TAUT A

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

assume that

A1: p in TAUT A and

A2: q in TAUT A ; :: thesis: p '&' q in TAUT A

p => (q => (p '&' q)) in TAUT A by Th28;

then q => (p '&' q) in TAUT A by A1, CQC_THE1:46;

hence p '&' q in TAUT A by A2, CQC_THE1:46; :: thesis: verum