Theorem anbi2

Description: Introduce a left conjunct to both sides of a logical equivalence. (Contributed by NM, 16-Nov-2013)

	Ref	Expression
Assertion	anbi2	⊢ ( ( 𝜑 ↔ 𝜓 ) → ( ( 𝜒 ∧ 𝜑 ) ↔ ( 𝜒 ∧ 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( ( 𝜑 ↔ 𝜓 ) → ( 𝜑 ↔ 𝜓 ) )
2	1	anbi2d	⊢ ( ( 𝜑 ↔ 𝜓 ) → ( ( 𝜒 ∧ 𝜑 ) ↔ ( 𝜒 ∧ 𝜓 ) ) )