let A be QC-alphabet ; :: thesis: for p, q being Element of CQC-WFF A st p 'or' q in TAUT A & 'not' p in TAUT A holds
q in TAUT A
let p, q be Element of CQC-WFF A; :: thesis: ( p 'or' q in TAUT A & 'not' p in TAUT A implies q in TAUT A )
assume that
A1: p 'or' q in TAUT A and
A2: 'not' p in TAUT A ; :: thesis: q in TAUT A
(p 'or' q) => (('not' p) => q) in TAUT A by Th5;
then ('not' p) => q in TAUT A by A1, CQC_THE1:46;
hence q in TAUT A by A2, CQC_THE1:46; :: thesis: verum