let p, q, r, s be Element of CQC-WFF ; :: thesis: ( p => q in TAUT & r => s in TAUT implies (p '&' r) => (q '&' s) in TAUT )
assume that
A1: p => q in TAUT and
A2: r => s in TAUT ; :: thesis: (p '&' r) => (q '&' s) in TAUT
A3: (p '&' r) => (q '&' r) in TAUT by A1, Th51;
(q '&' r) => (q '&' s) in TAUT by A2, Lm5;
hence (p '&' r) => (q '&' s) in TAUT by A3, LUKASI_1:3; :: thesis: verum