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

q in TAUT A

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

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

(p '&' q) => q in TAUT A by Th21;

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

q in TAUT A

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

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

(p '&' q) => q in TAUT A by Th21;

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