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Metamath Proof Explorer

Theorem bitr

Description: Theorem *4.22 of WhiteheadRussell p. 117. bitri in closed form. (Contributed by NM, 3-Jan-2005)

Ref Expression
Assertion bitr ⊢ φ ↔ ψ ∧ ψ ↔ χ → φ ↔ χ

Proof

Step Hyp Ref Expression
1 bibi1 ⊢ φ ↔ ψ → φ ↔ χ ↔ ψ ↔ χ
2 1 biimpar ⊢ φ ↔ ψ ∧ ψ ↔ χ → φ ↔ χ