let p, q be Element of CQC-WFF ; :: thesis: (p '&' q) => ('not' (p => ('not' q))) in TAUT
A1: (p '&' ('not' ('not' q))) => ('not' ('not' (p '&' ('not' ('not' q))))) in TAUT by LUKASI_1:27;
( (q '&' p) => (('not' ('not' q)) '&' p) in TAUT & (p '&' q) => (q '&' p) in TAUT ) by Lm2, CQC_THE1:45;
then A2: (p '&' q) => (('not' ('not' q)) '&' p) in TAUT by LUKASI_1:3;
(('not' ('not' q)) '&' p) => (p '&' ('not' ('not' q))) in TAUT by CQC_THE1:45;
then (p '&' q) => (p '&' ('not' ('not' q))) in TAUT by A2, LUKASI_1:3;
then (p '&' q) => ('not' ('not' (p '&' ('not' ('not' q))))) in TAUT by A1, LUKASI_1:3;
hence (p '&' q) => ('not' (p => ('not' q))) in TAUT by QC_LANG2:def 2; :: thesis: verum