Theorem pm1.5

Description: Axiom *1.5 (Assoc) of WhiteheadRussell p. 96. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm1.5	$$⊢\left(\phi \vee \left(\psi \vee \chi \right)\right)\to \left(\psi \vee \left(\phi \vee \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		orc	$$⊢\phi \to \left(\phi \vee \chi \right)$$
2	1	olcd	$$⊢\phi \to \left(\psi \vee \left(\phi \vee \chi \right)\right)$$
3		olc	$$⊢\chi \to \left(\phi \vee \chi \right)$$
4	3	orim2i	$$⊢\left(\psi \vee \chi \right)\to \left(\psi \vee \left(\phi \vee \chi \right)\right)$$
5	2 4	jaoi	$$⊢\left(\phi \vee \left(\psi \vee \chi \right)\right)\to \left(\psi \vee \left(\phi \vee \chi \right)\right)$$