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Metamath Proof Explorer

Theorem bitr3i

Description: An inference from transitive law for logical equivalence. (Contributed by NM, 2-Jun-1993)

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

Proof

Step Hyp Ref Expression
1 bitr3i.1 ⊢ ψ ↔ φ
2 bitr3i.2 ⊢ ψ ↔ χ
3 1 bicomi ⊢ φ ↔ ψ
4 3 2 bitri ⊢ φ ↔ χ