Metamath Proof Explorer

Theorem imbi2

Description: Theorem *4.85 of WhiteheadRussell p. 122. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 19-May-2013)

Ref Expression
Assertion imbi2 ( ( 𝜑 ↔ 𝜓 ) → ( ( 𝜒 → 𝜑 ) ↔ ( 𝜒 → 𝜓 ) ) )

Proof

Step Hyp Ref Expression
1 id ⊢ ( ( 𝜑 ↔ 𝜓 ) → ( 𝜑 ↔ 𝜓 ) )
2 1 imbi2d ⊢ ( ( 𝜑 ↔ 𝜓 ) → ( ( 𝜒 → 𝜑 ) ↔ ( 𝜒 → 𝜓 ) ) )