let A be QC-alphabet ; :: thesis: for p, q being Element of CQC-WFF A holds (p '&' q) => p in TAUT A
let p, q be Element of CQC-WFF A; :: thesis: (p '&' q) => p in TAUT A
('not' p) => (('not' p) 'or' ('not' q)) in TAUT A by Th3;
then A1: ('not' (('not' p) 'or' ('not' q))) => ('not' ('not' p)) in TAUT A by LUKASI_1:34;
(('not' p) 'or' ('not' q)) => ('not' (p '&' q)) in TAUT A by Th18;
then A2: ('not' ('not' (p '&' q))) => ('not' (('not' p) 'or' ('not' q))) in TAUT A by LUKASI_1:34;
(p '&' q) => ('not' ('not' (p '&' q))) in TAUT A by LUKASI_1:27;
then A3: (p '&' q) => ('not' (('not' p) 'or' ('not' q))) in TAUT A by A2, LUKASI_1:3;
('not' ('not' p)) => p in TAUT A by LUKASI_1:25;
then ('not' (('not' p) 'or' ('not' q))) => p in TAUT A by A1, LUKASI_1:3;
hence (p '&' q) => p in TAUT A by A3, LUKASI_1:3; :: thesis: verum