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

p => r is valid

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

assume p => (q => r) is valid ; :: thesis: ( not q is valid or p => r is valid )

then q => (p => r) is valid by Th44;

hence ( not q is valid or p => r is valid ) by 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 & q is valid implies p => r is valid )

assume p => (q => r) is valid ; :: thesis: ( not q is valid or p => r is valid )

then q => (p => r) is valid by Th44;

hence ( not q is valid or p => r is valid ) by CQC_THE1:65; :: thesis: verum