Theorem pm5.32i

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

	Ref	Expression
Hypothesis	pm5.32i.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
Assertion	pm5.32i	⊢ ( ( 𝜑 ∧ 𝜓 ) ↔ ( 𝜑 ∧ 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		pm5.32i.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
2		pm5.32	⊢ ( ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) ↔ ( ( 𝜑 ∧ 𝜓 ) ↔ ( 𝜑 ∧ 𝜒 ) ) )
3	1 2	mpbi	⊢ ( ( 𝜑 ∧ 𝜓 ) ↔ ( 𝜑 ∧ 𝜒 ) )