Theorem pm5.42

Description: Theorem *5.42 of WhiteheadRussell p. 125. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm5.42	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)\leftrightarrow \left(\phi \to \left(\psi \to \left(\phi \wedge \chi \right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		ibar	$$⊢\phi \to \left(\chi \leftrightarrow \left(\phi \wedge \chi \right)\right)$$
2	1	imbi2d	$$⊢\phi \to \left(\left(\psi \to \chi \right)\leftrightarrow \left(\psi \to \left(\phi \wedge \chi \right)\right)\right)$$
3	2	pm5.74i	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)\leftrightarrow \left(\phi \to \left(\psi \to \left(\phi \wedge \chi \right)\right)\right)$$