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 φ ψ
3bitr2i.2 χ ψ
3bitr2i.3 χ θ
Assertion 3bitr2i φ θ

Proof

Step Hyp Ref Expression
1 3bitr2i.1 φ ψ
2 3bitr2i.2 χ ψ
3 3bitr2i.3 χ θ
4 1 2 bitr4i φ χ
5 4 3 bitri φ θ