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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