Theorem pm5.74ri

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

	Ref	Expression
Hypothesis	pm5.74ri.1	$$⊢\left(\phi \to \psi \right)\leftrightarrow \left(\phi \to \chi \right)$$
Assertion	pm5.74ri	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		pm5.74ri.1	$$⊢\left(\phi \to \psi \right)\leftrightarrow \left(\phi \to \chi \right)$$
2		pm5.74	$$⊢\left(\phi \to \left(\psi \leftrightarrow \chi \right)\right)\leftrightarrow \left(\left(\phi \to \psi \right)\leftrightarrow \left(\phi \to \chi \right)\right)$$
3	1 2	mpbir	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$