Theorem pm2.8

Description: Theorem *2.8 of WhiteheadRussell p. 108. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 5-Jan-2013)

	Ref	Expression
Assertion	pm2.8	$$⊢\left(\phi \vee \psi \right)\to \left(\left(\neg \psi \vee \chi \right)\to \left(\phi \vee \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		pm2.53	$$⊢\left(\phi \vee \psi \right)\to \left(\neg \phi \to \psi \right)$$
2	1	con1d	$$⊢\left(\phi \vee \psi \right)\to \left(\neg \psi \to \phi \right)$$
3	2	orim1d	$$⊢\left(\phi \vee \psi \right)\to \left(\left(\neg \psi \vee \chi \right)\to \left(\phi \vee \chi \right)\right)$$