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

q => r is valid

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

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

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

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

q => r is valid

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

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

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

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