Theorem 3bitr3i

Description: A chained inference from transitive law for logical equivalence. (Contributed by NM, 19-Aug-1993)

	Ref	Expression
Hypotheses	3bitr3i.1	⊢ ( 𝜑 ↔ 𝜓 )
	3bitr3i.2	⊢ ( 𝜑 ↔ 𝜒 )
	3bitr3i.3	⊢ ( 𝜓 ↔ 𝜃 )
Assertion	3bitr3i	⊢ ( 𝜒 ↔ 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		3bitr3i.1	⊢ ( 𝜑 ↔ 𝜓 )
2		3bitr3i.2	⊢ ( 𝜑 ↔ 𝜒 )
3		3bitr3i.3	⊢ ( 𝜓 ↔ 𝜃 )
4	2 1	bitr3i	⊢ ( 𝜒 ↔ 𝜓 )
5	4 3	bitri	⊢ ( 𝜒 ↔ 𝜃 )