Metamath Proof Explorer

Theorem imbi1

Description: Theorem *4.84 of WhiteheadRussell p. 122. (Contributed by NM, 3-Jan-2005)

Ref Expression
Assertion imbi1 ( ( 𝜑 ↔ 𝜓 ) → ( ( 𝜑 → 𝜒 ) ↔ ( 𝜓 → 𝜒 ) ) )

Proof

Step Hyp Ref Expression
1 id ⊢ ( ( 𝜑 ↔ 𝜓 ) → ( 𝜑 ↔ 𝜓 ) )
2 1 imbi1d ⊢ ( ( 𝜑 ↔ 𝜓 ) → ( ( 𝜑 → 𝜒 ) ↔ ( 𝜓 → 𝜒 ) ) )