let p, q, r be Element of CQC-WFF ; :: thesis: ( p => q in TAUT implies (r 'or' p) => (r 'or' q) in TAUT )
assume p => q in TAUT ; :: thesis: (r 'or' p) => (r 'or' q) in TAUT
then A1: ('not' r) => (p => q) in TAUT by LUKASI_1:13;
(('not' r) => (p => q)) => ((('not' r) => p) => (('not' r) => q)) in TAUT by LUKASI_1:11;
then (('not' r) => p) => (('not' r) => q) in TAUT by A1, CQC_THE1:46;
then (r 'or' p) => (('not' r) => q) in TAUT by Lm1;
hence (r 'or' p) => (r 'or' q) in TAUT by Lm1; :: thesis: verum