Theorem pm2.85

Description: Theorem *2.85 of WhiteheadRussell p. 108. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 5-Jan-2013)

	Ref	Expression
Assertion	pm2.85	$$⊢\left(\left(\phi \vee \psi \right)\to \left(\phi \vee \chi \right)\right)\to \left(\phi \vee \left(\psi \to \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		orimdi	$$⊢\left(\phi \vee \left(\psi \to \chi \right)\right)\leftrightarrow \left(\left(\phi \vee \psi \right)\to \left(\phi \vee \chi \right)\right)$$
2	1	biimpri	$$⊢\left(\left(\phi \vee \psi \right)\to \left(\phi \vee \chi \right)\right)\to \left(\phi \vee \left(\psi \to \chi \right)\right)$$