Theorem orel1

Description: Elimination of disjunction by denial of a disjunct. Theorem *2.55 of WhiteheadRussell p. 107. (Contributed by NM, 12-Aug-1994) (Proof shortened by Wolf Lammen, 21-Jul-2012)

	Ref	Expression
Assertion	orel1	⊢ ( ¬ 𝜑 → ( ( 𝜑 ∨ 𝜓 ) → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		pm2.53	⊢ ( ( 𝜑 ∨ 𝜓 ) → ( ¬ 𝜑 → 𝜓 ) )
2	1	com12	⊢ ( ¬ 𝜑 → ( ( 𝜑 ∨ 𝜓 ) → 𝜓 ) )