let A be QC-alphabet ; :: thesis: for p, q, r being Element of CQC-WFF A st p => q is valid & r => q is valid holds
(p 'or' r) => q is valid
let p, q, r be Element of CQC-WFF A; :: thesis: ( p => q is valid & r => q is valid implies (p 'or' r) => q is valid )
assume ( p => q in TAUT A & r => q in TAUT A ) ; :: according to CQC_THE1:def 10 :: thesis: (p 'or' r) => q is valid
hence (p 'or' r) => q in TAUT A by PROCAL_1:53; :: according to CQC_THE1:def 10 :: thesis: verum