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

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

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

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

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

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

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

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

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

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

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