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 'or' r) => (q 'or' 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 'or' r) => (q 'or' s) in TAUT A )
assume ( p => q in TAUT A & r => s in TAUT A ) ; :: thesis: (p 'or' r) => (q 'or' s) in TAUT A
then ( (p 'or' r) => (q 'or' r) in TAUT A & (q 'or' r) => (q 'or' s) in TAUT A ) by Lm6, Lm7;
hence (p 'or' r) => (q 'or' s) in TAUT A by LUKASI_1:3; :: thesis: verum