let A be QC-alphabet ; :: thesis: for p, q being Element of CQC-WFF A holds (('not' ('not' p)) '&' q) => (p '&' q) in TAUT A
let p, q be Element of CQC-WFF A; :: thesis: (('not' ('not' p)) '&' q) => (p '&' q) in TAUT A
( (('not' ('not' p)) => p) => (('not' (p '&' q)) => ('not' (('not' ('not' p)) '&' q))) in TAUT A & ('not' ('not' p)) => p in TAUT A ) by CQC_THE1:44, LUKASI_1:25;
then ('not' (p '&' q)) => ('not' (('not' ('not' p)) '&' q)) in TAUT A by CQC_THE1:46;
hence (('not' ('not' p)) '&' q) => (p '&' q) in TAUT A by LUKASI_1:35; :: thesis: verum