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

(q => r) => (p => r) is valid

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

assume A1: p => q is valid ; :: thesis: (q => r) => (p => r) is valid

(p => q) => ((q => r) => (p => r)) is valid ;

hence (q => r) => (p => r) is valid by A1, CQC_THE1:65; :: thesis: verum

(q => r) => (p => r) is valid

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

assume A1: p => q is valid ; :: thesis: (q => r) => (p => r) is valid

(p => q) => ((q => r) => (p => r)) is valid ;

hence (q => r) => (p => r) is valid by A1, CQC_THE1:65; :: thesis: verum