let p, q, r be Element of CQC-WFF ; :: thesis: ( p => q in TAUT implies (p 'or' r) => (q 'or' r) in TAUT )
assume p => q in TAUT ; :: thesis: (p 'or' r) => (q 'or' r) in TAUT
then A1: ('not' q) => ('not' p) in TAUT by LUKASI_1:34;
(('not' q) => ('not' p)) => ((('not' p) => r) => (('not' q) => r)) in TAUT by LUKASI_1:1;
then (('not' p) => r) => (('not' q) => r) in TAUT by A1, CQC_THE1:82;
then (p 'or' r) => (('not' q) => r) in TAUT by Lm1;
hence (p 'or' r) => (q 'or' r) in TAUT by Lm1; :: thesis: verum