let A be QC-alphabet ; :: thesis: for p, q being Element of CQC-WFF A holds (('not' p) => ('not' q)) => (q => p) in TAUT A
let p, q be Element of CQC-WFF A; :: thesis: (('not' p) => ('not' q)) => (q => p) in TAUT A
( q => (('not' q) => ('not' (VERUM A))) in TAUT A & (('not' q) => ('not' (VERUM A))) => ((('not' p) => ('not' q)) => (('not' p) => ('not' (VERUM A)))) in TAUT A ) by Th9, CQC_THE1:43;
then A1: q => ((('not' p) => ('not' q)) => (('not' p) => ('not' (VERUM A)))) in TAUT A by Th3;
q => ((('not' p) => ('not' (VERUM A))) => p) in TAUT A by Lm24, Th13;
then q => ((('not' p) => ('not' q)) => p) in TAUT A by A1, Th22;
hence (('not' p) => ('not' q)) => (q => p) in TAUT A by Th15; :: thesis: verum