let p, q be Element of CQC-WFF ; :: thesis: ( (p '&' ('not' q)) => ('not' p) in TAUT implies p => q in TAUT )
A1: 'not' (p '&' ('not' q)) = p => q by QC_LANG2:def 2;
assume (p '&' ('not' q)) => ('not' p) in TAUT ; :: thesis: p => q in TAUT
then A2: ('not' ('not' p)) => ('not' (p '&' ('not' q))) in TAUT by LUKASI_1:34;
p => ('not' ('not' p)) in TAUT by LUKASI_1:27;
then p => ('not' (p '&' ('not' q))) in TAUT by A2, LUKASI_1:3;
hence p => q in TAUT by A1, LUKASI_1:18; :: thesis: verum