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Metamath Proof Explorer

Theorem 3bitr2i

Description: A chained inference from transitive law for logical equivalence. (Contributed by NM, 4-Aug-2006)

Ref Expression
Hypotheses 3bitr2i.1 ⊢ φ ↔ ψ
3bitr2i.2 ⊢ χ ↔ ψ
3bitr2i.3 ⊢ χ ↔ θ
Assertion 3bitr2i ⊢ φ ↔ θ

Proof

Step Hyp Ref Expression
1 3bitr2i.1 ⊢ φ ↔ ψ
2 3bitr2i.2 ⊢ χ ↔ ψ
3 3bitr2i.3 ⊢ χ ↔ θ
4 1 2 bitr4i ⊢ φ ↔ χ
5 4 3 bitri ⊢ φ ↔ θ