let A be QC-alphabet ; :: thesis: for p, q being Element of CQC-WFF A holds
( (p => ('not' ('not' q))) => (p => q) in TAUT A & (p => q) => (p => ('not' ('not' q))) in TAUT A )
let p, q be Element of CQC-WFF A; :: thesis: ( (p => ('not' ('not' q))) => (p => q) in TAUT A & (p => q) => (p => ('not' ('not' q))) in TAUT A )
( (p => (('not' ('not' q)) => q)) => ((p => ('not' ('not' q))) => (p => q)) in TAUT A & p => (('not' ('not' q)) => q) in TAUT A ) by Th11, Th13, Th25;
hence (p => ('not' ('not' q))) => (p => q) in TAUT A by CQC_THE1:46; :: thesis: (p => q) => (p => ('not' ('not' q))) in TAUT A
( (p => (q => ('not' ('not' q)))) => ((p => q) => (p => ('not' ('not' q)))) in TAUT A & p => (q => ('not' ('not' q))) in TAUT A ) by Th11, Th13, Th27;
hence (p => q) => (p => ('not' ('not' q))) in TAUT A by CQC_THE1:46; :: thesis: verum