let A be QC-alphabet ; :: thesis: for p, q being Element of CQC-WFF A holds (p '&' q) => (('not' ('not' p)) '&' q) in TAUT A
let p, q be Element of CQC-WFF A; :: thesis: (p '&' q) => (('not' ('not' p)) '&' q) in TAUT A
( (p => ('not' ('not' p))) => (('not' (('not' ('not' p)) '&' q)) => ('not' (p '&' q))) in TAUT A & p => ('not' ('not' p)) in TAUT A ) by CQC_THE1:44, LUKASI_1:27;
then ('not' (('not' ('not' p)) '&' q)) => ('not' (p '&' q)) in TAUT A by CQC_THE1:46;
hence (p '&' q) => (('not' ('not' p)) '&' q) in TAUT A by LUKASI_1:35; :: thesis: verum