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

(q => r) => (p => r) in TAUT A

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

assume A1: p => q in TAUT A ; :: thesis: (q => r) => (p => r) in TAUT A

(p => q) => ((q => r) => (p => r)) in TAUT A by Th1;

hence (q => r) => (p => r) in TAUT A by A1, CQC_THE1:46; :: thesis: verum

(q => r) => (p => r) in TAUT A

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

assume A1: p => q in TAUT A ; :: thesis: (q => r) => (p => r) in TAUT A

(p => q) => ((q => r) => (p => r)) in TAUT A by Th1;

hence (q => r) => (p => r) in TAUT A by A1, CQC_THE1:46; :: thesis: verum