Theorem bitr2i

Description: An inference from transitive law for logical equivalence. (Contributed by NM, 12-Mar-1993)

	Ref	Expression
Hypotheses	bitr2i.1	⊢ ( 𝜑 ↔ 𝜓 )
	bitr2i.2	⊢ ( 𝜓 ↔ 𝜒 )
Assertion	bitr2i	⊢ ( 𝜒 ↔ 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		bitr2i.1	⊢ ( 𝜑 ↔ 𝜓 )
2		bitr2i.2	⊢ ( 𝜓 ↔ 𝜒 )
3	1 2	bitri	⊢ ( 𝜑 ↔ 𝜒 )
4	3	bicomi	⊢ ( 𝜒 ↔ 𝜑 )