Theorem bitr3i

Description: An inference from transitive law for logical equivalence. (Contributed by NM, 2-Jun-1993)

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

Proof

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