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