Metamath Proof Explorer


Theorem 3bitr2i

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 3bitr2i φθ

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 bitri φθ