Theorem anbi1

Description: Introduce a right conjunct to both sides of a logical equivalence. Theorem *4.36 of WhiteheadRussell p. 118. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	anbi1	⊢ ( ( 𝜑 ↔ 𝜓 ) → ( ( 𝜑 ∧ 𝜒 ) ↔ ( 𝜓 ∧ 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( ( 𝜑 ↔ 𝜓 ) → ( 𝜑 ↔ 𝜓 ) )
2	1	anbi1d	⊢ ( ( 𝜑 ↔ 𝜓 ) → ( ( 𝜑 ∧ 𝜒 ) ↔ ( 𝜓 ∧ 𝜒 ) ) )