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

Metamath Proof Explorer

Theorem 3bitrri

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

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

Proof

Step Hyp Ref Expression
1 3bitri.1 ⊢ ( 𝜑 ↔ 𝜓 )
2 3bitri.2 ⊢ ( 𝜓 ↔ 𝜒 )
3 3bitri.3 ⊢ ( 𝜒 ↔ 𝜃 )
4 1 2 bitr2i ⊢ ( 𝜒 ↔ 𝜑 )
5 3 4 bitr3i ⊢ ( 𝜃 ↔ 𝜑 )