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	$$⊢\neg \phi \to \left(\left(\phi \vee \psi \right)\to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		pm2.53	$$⊢\left(\phi \vee \psi \right)\to \left(\neg \phi \to \psi \right)$$
2	1	com12	$$⊢\neg \phi \to \left(\left(\phi \vee \psi \right)\to \psi \right)$$