Theorem pm4.71da

Description: Deduction converting a biconditional to a biconditional with conjunction. Variant of pm4.71d . (Contributed by Zhi Wang, 30-Aug-2024)

	Ref	Expression
Hypothesis	pm4.71da.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
Assertion	pm4.71da	$$⊢\phi \to \left(\psi \leftrightarrow \left(\psi \wedge \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		pm4.71da.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
2	1	biimpd	$$⊢\phi \to \left(\psi \to \chi \right)$$
3	2	pm4.71d	$$⊢\phi \to \left(\psi \leftrightarrow \left(\psi \wedge \chi \right)\right)$$