Metamath Proof Explorer


Theorem 3bitr3ri

Description: A chained inference from transitive law for logical equivalence. (Contributed by NM, 21-Jun-1993)

Ref Expression
Hypotheses 3bitr3i.1 φ ψ
3bitr3i.2 φ χ
3bitr3i.3 ψ θ
Assertion 3bitr3ri θ χ

Proof

Step Hyp Ref Expression
1 3bitr3i.1 φ ψ
2 3bitr3i.2 φ χ
3 3bitr3i.3 ψ θ
4 1 2 bitr3i ψ χ
5 3 4 bitr3i θ χ