Theorem bitr4i

Description: An inference from transitive law for logical equivalence. (Contributed by NM, 3-Jan-1993)

	Ref	Expression
Hypotheses	bitr4i.1	⊢ ( 𝜑 ↔ 𝜓 )
	bitr4i.2	⊢ ( 𝜒 ↔ 𝜓 )
Assertion	bitr4i	⊢ ( 𝜑 ↔ 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		bitr4i.1	⊢ ( 𝜑 ↔ 𝜓 )
2		bitr4i.2	⊢ ( 𝜒 ↔ 𝜓 )
3	2	bicomi	⊢ ( 𝜓 ↔ 𝜒 )
4	1 3	bitri	⊢ ( 𝜑 ↔ 𝜒 )