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	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
Assertion	pm4.71da	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜓 ∧ 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		pm4.71da.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
2	1	biimpd	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
3	2	pm4.71d	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜓 ∧ 𝜒 ) ) )