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Metamath Proof Explorer

Theorem bitr4i

Description: An inference from transitive law for logical equivalence. (Contributed by NM, 3-Jan-1993)

Ref Expression
Hypotheses bitr4i.1 ⊢ φ ↔ ψ
bitr4i.2 ⊢ χ ↔ ψ
Assertion bitr4i ⊢ φ ↔ χ

Proof

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