let A be QC-alphabet ; :: thesis: for p, q being Element of CQC-WFF A holds ('not' (p '&' q)) => (('not' p) 'or' ('not' q)) in TAUT A
let p, q be Element of CQC-WFF A; :: thesis: ('not' (p '&' q)) => (('not' p) 'or' ('not' q)) in TAUT A
( ('not' ('not' p)) => p in TAUT A & (('not' ('not' p)) => p) => ((p => ('not' q)) => (('not' ('not' p)) => ('not' q))) in TAUT A ) by LUKASI_1:1, LUKASI_1:25;
then A1: (p => ('not' q)) => (('not' ('not' p)) => ('not' q)) in TAUT A by CQC_THE1:46;
('not' (p => ('not' q))) => (p '&' q) in TAUT A by Th16;
then A2: ('not' (p '&' q)) => ('not' ('not' (p => ('not' q)))) in TAUT A by LUKASI_1:34;
('not' ('not' (p => ('not' q)))) => (p => ('not' q)) in TAUT A by LUKASI_1:25;
then ('not' (p '&' q)) => (p => ('not' q)) in TAUT A by A2, LUKASI_1:3;
then ('not' (p '&' q)) => (('not' ('not' p)) => ('not' q)) in TAUT A by A1, LUKASI_1:3;
hence ('not' (p '&' q)) => (('not' p) 'or' ('not' q)) in TAUT A by Lm1; :: thesis: verum