Theorem pm2.31

Description: Theorem *2.31 of WhiteheadRussell p. 104. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm2.31	$$⊢\left(\phi \vee \left(\psi \vee \chi \right)\right)\to \left(\left(\phi \vee \psi \right)\vee \chi \right)$$

Proof

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