let A be QC-alphabet ; :: thesis: for p, q, r being Element of CQC-WFF A st p => q in TAUT A holds
(p 'or' r) => (q 'or' r) in TAUT A
let p, q, r be Element of CQC-WFF A; :: thesis: ( p => q in TAUT A implies (p 'or' r) => (q 'or' r) in TAUT A )
assume p => q in TAUT A ; :: thesis: (p 'or' r) => (q 'or' r) in TAUT A
then A1: ('not' q) => ('not' p) in TAUT A by LUKASI_1:34;
(('not' q) => ('not' p)) => ((('not' p) => r) => (('not' q) => r)) in TAUT A by LUKASI_1:1;
then (('not' p) => r) => (('not' q) => r) in TAUT A by A1, CQC_THE1:46;
then (p 'or' r) => (('not' q) => r) in TAUT A by Lm1;
hence (p 'or' r) => (q 'or' r) in TAUT A by Lm1; :: thesis: verum