Theorem pm5.44

Description: Theorem *5.44 of WhiteheadRussell p. 125. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm5.44	$$⊢\left(\phi \to \psi \right)\to \left(\left(\phi \to \chi \right)\leftrightarrow \left(\phi \to \left(\psi \wedge \chi \right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		jcab	$$⊢\left(\phi \to \left(\psi \wedge \chi \right)\right)\leftrightarrow \left(\left(\phi \to \psi \right)\wedge \left(\phi \to \chi \right)\right)$$
2	1	baibr	$$⊢\left(\phi \to \psi \right)\to \left(\left(\phi \to \chi \right)\leftrightarrow \left(\phi \to \left(\psi \wedge \chi \right)\right)\right)$$