This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem 3bitr3i

Description: A chained inference from transitive law for logical equivalence. (Contributed by NM, 19-Aug-1993)

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

Proof

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