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

q => r is valid

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

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

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

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

q => r is valid

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

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

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

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