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

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

( p => (p 'or' q) in TAUT A & (p '&' q) => p in TAUT A ) by Th3, Th19;

hence (p '&' q) => (p 'or' q) in TAUT A by LUKASI_1:3; :: thesis: verum

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

( p => (p 'or' q) in TAUT A & (p '&' q) => p in TAUT A ) by Th3, Th19;

hence (p '&' q) => (p 'or' q) in TAUT A by LUKASI_1:3; :: thesis: verum