let A be QC-alphabet ; :: thesis: for p, q, r being Element of CQC-WFF A st p => q in TAUT A holds
(r 'or' p) => (r 'or' q) in TAUT A
let p, q, r be Element of CQC-WFF A; :: thesis: ( p => q in TAUT A implies (r 'or' p) => (r 'or' q) in TAUT A )
assume p => q in TAUT A ; :: thesis: (r 'or' p) => (r 'or' q) in TAUT A
then A1: ('not' r) => (p => q) in TAUT A by LUKASI_1:13;
(('not' r) => (p => q)) => ((('not' r) => p) => (('not' r) => q)) in TAUT A by LUKASI_1:11;
then (('not' r) => p) => (('not' r) => q) in TAUT A by A1, CQC_THE1:46;
then (r 'or' p) => (('not' r) => q) in TAUT A by Lm1;
hence (r 'or' p) => (r 'or' q) in TAUT A by Lm1; :: thesis: verum