Metamath Proof Explorer


Theorem 3bitr2ri

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

Ref Expression
Hypotheses 3bitr2i.1 ( 𝜑𝜓 )
3bitr2i.2 ( 𝜒𝜓 )
3bitr2i.3 ( 𝜒𝜃 )
Assertion 3bitr2ri ( 𝜃𝜑 )

Proof

Step Hyp Ref Expression
1 3bitr2i.1 ( 𝜑𝜓 )
2 3bitr2i.2 ( 𝜒𝜓 )
3 3bitr2i.3 ( 𝜒𝜃 )
4 1 2 bitr4i ( 𝜑𝜒 )
5 4 3 bitr2i ( 𝜃𝜑 )