This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

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