Theorem pm3.43

Description: Theorem *3.43 (Comp) of WhiteheadRussell p. 113. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm3.43	$$⊢\left(\left(\phi \to \psi \right)\wedge \left(\phi \to \chi \right)\right)\to \left(\phi \to \left(\psi \wedge \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		pm3.43i	$$⊢\left(\phi \to \psi \right)\to \left(\left(\phi \to \chi \right)\to \left(\phi \to \left(\psi \wedge \chi \right)\right)\right)$$
2	1	imp	$$⊢\left(\left(\phi \to \psi \right)\wedge \left(\phi \to \chi \right)\right)\to \left(\phi \to \left(\psi \wedge \chi \right)\right)$$