let A be QC-alphabet ; :: thesis: for p, q, r, s being Element of CQC-WFF A st p => q in TAUT A & r => s in TAUT A holds
(p '&' r) => (q '&' s) in TAUT A
let p, q, r, s be Element of CQC-WFF A; :: thesis: ( p => q in TAUT A & r => s in TAUT A implies (p '&' r) => (q '&' s) in TAUT A )
assume ( p => q in TAUT A & r => s in TAUT A ) ; :: thesis: (p '&' r) => (q '&' s) in TAUT A
then ( (p '&' r) => (q '&' r) in TAUT A & (q '&' r) => (q '&' s) in TAUT A ) by Lm5, Th51;
hence (p '&' r) => (q '&' s) in TAUT A by LUKASI_1:3; :: thesis: verum