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Metamath Proof Explorer

Theorem 3bitr3ri

Description: A chained inference from transitive law for logical equivalence. (Contributed by NM, 21-Jun-1993)

Ref Expression
Hypotheses 3bitr3i.1 ⊢ φ ↔ ψ
3bitr3i.2 ⊢ φ ↔ χ
3bitr3i.3 ⊢ ψ ↔ θ
Assertion 3bitr3ri ⊢ θ ↔ χ

Proof

Step Hyp Ref Expression
1 3bitr3i.1 ⊢ φ ↔ ψ
2 3bitr3i.2 ⊢ φ ↔ χ
3 3bitr3i.3 ⊢ ψ ↔ θ
4 1 2 bitr3i ⊢ ψ ↔ χ
5 3 4 bitr3i ⊢ θ ↔ χ