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 )