let p, q be Element of CQC-WFF ; :: thesis: ('not' (p => ('not' q))) => (p '&' q) in TAUT
A1: ('not' ('not' (p '&' ('not' ('not' q))))) => (p '&' ('not' ('not' q))) in TAUT by LUKASI_1:25;
( (p '&' ('not' ('not' q))) => (('not' ('not' q)) '&' p) in TAUT & (('not' ('not' q)) '&' p) => (q '&' p) in TAUT ) by Lm3, CQC_THE1:81;
then A2: (p '&' ('not' ('not' q))) => (q '&' p) in TAUT by LUKASI_1:3;
(q '&' p) => (p '&' q) in TAUT by CQC_THE1:81;
then (p '&' ('not' ('not' q))) => (p '&' q) in TAUT by A2, LUKASI_1:3;
then ('not' ('not' (p '&' ('not' ('not' q))))) => (p '&' q) in TAUT by A1, LUKASI_1:3;
hence ('not' (p => ('not' q))) => (p '&' q) in TAUT by QC_LANG2:def 2; :: thesis: verum