Theorem pm3.48

Description: Theorem *3.48 of WhiteheadRussell p. 114. (Contributed by NM, 28-Jan-1997)

	Ref	Expression
Assertion	pm3.48	$$⊢\left(\left(\phi \to \psi \right)\wedge \left(\chi \to \theta \right)\right)\to \left(\left(\phi \vee \chi \right)\to \left(\psi \vee \theta \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		orc	$$⊢\psi \to \left(\psi \vee \theta \right)$$
2	1	imim2i	$$⊢\left(\phi \to \psi \right)\to \left(\phi \to \left(\psi \vee \theta \right)\right)$$
3		olc	$$⊢\theta \to \left(\psi \vee \theta \right)$$
4	3	imim2i	$$⊢\left(\chi \to \theta \right)\to \left(\chi \to \left(\psi \vee \theta \right)\right)$$
5	2 4	jaao	$$⊢\left(\left(\phi \to \psi \right)\wedge \left(\chi \to \theta \right)\right)\to \left(\left(\phi \vee \chi \right)\to \left(\psi \vee \theta \right)\right)$$