let p, q, r be Element of CQC-WFF ; :: thesis: ( p => q is valid & r => q is valid implies (p 'or' r) => q is valid )
assume ( p => q in TAUT & r => q in TAUT ) ; :: according to CQC_THE1:def 11 :: thesis: (p 'or' r) => q is valid
hence (p 'or' r) => q in TAUT by PROCAL_1:53; :: according to CQC_THE1:def 11 :: thesis: verum