Theorem pm5.32ri

Description: Distribution of implication over biconditional (inference form). (Contributed by NM, 12-Mar-1995)

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

Proof

Step	Hyp	Ref	Expression
1		pm5.32i.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
2	1	pm5.32i	$$⊢\left(\phi \wedge \psi \right)\leftrightarrow \left(\phi \wedge \chi \right)$$
3		ancom	$$⊢\left(\psi \wedge \phi \right)\leftrightarrow \left(\phi \wedge \psi \right)$$
4		ancom	$$⊢\left(\chi \wedge \phi \right)\leftrightarrow \left(\phi \wedge \chi \right)$$
5	2 3 4	3bitr4i	$$⊢\left(\psi \wedge \phi \right)\leftrightarrow \left(\chi \wedge \phi \right)$$