let A be QC-alphabet ; :: thesis: for p, q being Element of CQC-WFF A holds q => (p => q) in TAUT A

let p, q be Element of CQC-WFF A; :: thesis: q => (p => q) in TAUT A

( q => ((('not' p) => q) => q) in TAUT A & (q => ((('not' p) => q) => q)) => ((p => (('not' p) => q)) => (q => (p => q))) in TAUT A ) by Lm2, Lm12;

then ( p => (('not' p) => q) in TAUT A & (p => (('not' p) => q)) => (q => (p => q)) in TAUT A ) by CQC_THE1:43, CQC_THE1:46;

hence q => (p => q) in TAUT A by CQC_THE1:46; :: thesis: verum

let p, q be Element of CQC-WFF A; :: thesis: q => (p => q) in TAUT A

( q => ((('not' p) => q) => q) in TAUT A & (q => ((('not' p) => q) => q)) => ((p => (('not' p) => q)) => (q => (p => q))) in TAUT A ) by Lm2, Lm12;

then ( p => (('not' p) => q) in TAUT A & (p => (('not' p) => q)) => (q => (p => q)) in TAUT A ) by CQC_THE1:43, CQC_THE1:46;

hence q => (p => q) in TAUT A by CQC_THE1:46; :: thesis: verum