Theorem anbi2 646

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

Assertion

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

Proof of Theorem anbi2

Step	Hyp	Ref	Expression
1		id 23	. 2 ⊢ ((𝜑 ↔ 𝜓) → (𝜑 ↔ 𝜓))
2	1	anbi2d 642	1 ⊢ ((𝜑 ↔ 𝜓) → ((𝜒 ∧ 𝜑) ↔ (𝜒 ∧ 𝜓)))

This proof depends on syntax axioms:   → wi 4   ↔ wb 209   ∧ wa 401

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402

This theorem is used by:  eleq2d  2851