Theorem pm3.45

Description: Theorem *3.45 (Fact) of WhiteheadRussell p. 113. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm3.45	$$⊢\left(\phi \to \psi \right)\to \left(\left(\phi \wedge \chi \right)\to \left(\psi \wedge \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢\left(\phi \to \psi \right)\to \left(\phi \to \psi \right)$$
2	1	anim1d	$$⊢\left(\phi \to \psi \right)\to \left(\left(\phi \wedge \chi \right)\to \left(\psi \wedge \chi \right)\right)$$