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

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

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

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

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

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

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

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

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

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

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