Theorem pm2.42

Description: Theorem *2.42 of WhiteheadRussell p. 106. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm2.42	$$⊢\left(\neg \phi \vee \left(\phi \to \psi \right)\right)\to \left(\phi \to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		pm2.21	$$⊢\neg \phi \to \left(\phi \to \psi \right)$$
2		id	$$⊢\left(\phi \to \psi \right)\to \left(\phi \to \psi \right)$$
3	1 2	jaoi	$$⊢\left(\neg \phi \vee \left(\phi \to \psi \right)\right)\to \left(\phi \to \psi \right)$$