Theorem pm2.74

Description: Theorem *2.74 of WhiteheadRussell p. 108. (Contributed by NM, 3-Jan-2005) (Proof shortened by Andrew Salmon, 7-May-2011)

	Ref	Expression
Assertion	pm2.74	$$⊢\left(\psi \to \phi \right)\to \left(\left(\left(\phi \vee \psi \right)\vee \chi \right)\to \left(\phi \vee \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		orel2	$$⊢\neg \psi \to \left(\left(\phi \vee \psi \right)\to \phi \right)$$
2		ax-1	$$⊢\phi \to \left(\left(\phi \vee \psi \right)\to \phi \right)$$
3	1 2	ja	$$⊢\left(\psi \to \phi \right)\to \left(\left(\phi \vee \psi \right)\to \phi \right)$$
4	3	orim1d	$$⊢\left(\psi \to \phi \right)\to \left(\left(\left(\phi \vee \psi \right)\vee \chi \right)\to \left(\phi \vee \chi \right)\right)$$