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

p => r is valid

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

assume that

A1: p => (q => r) is valid and

A2: p => q is valid ; :: thesis: p => r is valid

(p => q) => (p => r) is valid by A1, Th48;

hence p => r is valid by A2, CQC_THE1:65; :: thesis: verum

p => r is valid

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

assume that

A1: p => (q => r) is valid and

A2: p => q is valid ; :: thesis: p => r is valid

(p => q) => (p => r) is valid by A1, Th48;

hence p => r is valid by A2, CQC_THE1:65; :: thesis: verum