Theorem pm5.32i

Description: Distribution of implication over biconditional (inference form). (Contributed by NM, 1-Aug-1994)

	Ref	Expression
Hypothesis	pm5.32i.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
Assertion	pm5.32i	$$⊢\left(\phi \wedge \psi \right)\leftrightarrow \left(\phi \wedge \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		pm5.32i.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
2		pm5.32	$$⊢\left(\phi \to \left(\psi \leftrightarrow \chi \right)\right)\leftrightarrow \left(\left(\phi \wedge \psi \right)\leftrightarrow \left(\phi \wedge \chi \right)\right)$$
3	1 2	mpbi	$$⊢\left(\phi \wedge \psi \right)\leftrightarrow \left(\phi \wedge \chi \right)$$