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

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

( (q => r) => (q => r) in TAUT A & ((q => r) => (q => r)) => ((q => (q => r)) => (q => r)) in TAUT A ) by Lm18, Th4;

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

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

( (q => r) => (q => r) in TAUT A & ((q => r) => (q => r)) => ((q => (q => r)) => (q => r)) in TAUT A ) by Lm18, Th4;

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