let p, q, r be Element of CQC-WFF ; :: thesis: ( p => q in TAUT implies (p '&' r) => (q '&' r) in TAUT )
A1: (p => q) => ((q => ('not' r)) => (p => ('not' r))) in TAUT by LUKASI_1:1;
assume p => q in TAUT ; :: thesis: (p '&' r) => (q '&' r) in TAUT
then (q => ('not' r)) => (p => ('not' r)) in TAUT by A1, CQC_THE1:46;
then A2: ('not' (p => ('not' r))) => ('not' (q => ('not' r))) in TAUT by LUKASI_1:34;
A3: ('not' (q => ('not' r))) => (q '&' r) in TAUT by Th16;
(p '&' r) => ('not' (p => ('not' r))) in TAUT by Th15;
then (p '&' r) => ('not' (q => ('not' r))) in TAUT by A2, LUKASI_1:3;
hence (p '&' r) => (q '&' r) in TAUT by A3, LUKASI_1:3; :: thesis: verum