let A be QC-alphabet ; :: thesis: for p, q being Element of CQC-WFF A holds (('not' p) 'or' ('not' q)) => ('not' (p '&' q)) in TAUT A
let p, q be Element of CQC-WFF A; :: thesis: (('not' p) 'or' ('not' q)) => ('not' (p '&' q)) in TAUT A
A1: (p => ('not' ('not' p))) => ((('not' ('not' p)) => ('not' q)) => (p => ('not' q))) in TAUT A by LUKASI_1:1;
(p '&' q) => ('not' (p => ('not' q))) in TAUT A by Th15;
then A2: ('not' ('not' (p => ('not' q)))) => ('not' (p '&' q)) in TAUT A by LUKASI_1:34;
(p => ('not' q)) => ('not' ('not' (p => ('not' q)))) in TAUT A by LUKASI_1:27;
then A3: (p => ('not' q)) => ('not' (p '&' q)) in TAUT A by A2, LUKASI_1:3;
( ('not' p) 'or' ('not' q) = ('not' ('not' p)) => ('not' q) & p => ('not' ('not' p)) in TAUT A ) by Lm1, LUKASI_1:27;
then (('not' p) 'or' ('not' q)) => (p => ('not' q)) in TAUT A by A1, CQC_THE1:46;
hence (('not' p) 'or' ('not' q)) => ('not' (p '&' q)) in TAUT A by A3, LUKASI_1:3; :: thesis: verum