let A be QC-alphabet ; :: thesis: for p, q, r being Element of CQC-WFF A st p => r in TAUT A & q => r in TAUT A holds

(p 'or' q) => r in TAUT A

let p, q, r be Element of CQC-WFF A; :: thesis: ( p => r in TAUT A & q => r in TAUT A implies (p 'or' q) => r in TAUT A )

assume ( p => r in TAUT A & q => r in TAUT A ) ; :: thesis: (p 'or' q) => r in TAUT A

then A1: (p => r) '&' (q => r) in TAUT A by Lm4;

((p => r) '&' (q => r)) => ((p 'or' q) => r) in TAUT A by Th36;

hence (p 'or' q) => r in TAUT A by A1, CQC_THE1:46; :: thesis: verum

(p 'or' q) => r in TAUT A

let p, q, r be Element of CQC-WFF A; :: thesis: ( p => r in TAUT A & q => r in TAUT A implies (p 'or' q) => r in TAUT A )

assume ( p => r in TAUT A & q => r in TAUT A ) ; :: thesis: (p 'or' q) => r in TAUT A

then A1: (p => r) '&' (q => r) in TAUT A by Lm4;

((p => r) '&' (q => r)) => ((p 'or' q) => r) in TAUT A by Th36;

hence (p 'or' q) => r in TAUT A by A1, CQC_THE1:46; :: thesis: verum