Theorem pm3.44

Description: Theorem *3.44 of WhiteheadRussell p. 113. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 3-Oct-2013)

	Ref	Expression
Assertion	pm3.44	$$⊢\left(\left(\psi \to \phi \right)\wedge \left(\chi \to \phi \right)\right)\to \left(\left(\psi \vee \chi \right)\to \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢\left(\psi \to \phi \right)\to \left(\psi \to \phi \right)$$
2		id	$$⊢\left(\chi \to \phi \right)\to \left(\chi \to \phi \right)$$
3	1 2	jaao	$$⊢\left(\left(\psi \to \phi \right)\wedge \left(\chi \to \phi \right)\right)\to \left(\left(\psi \vee \chi \right)\to \phi \right)$$