Theorem bitr4di

Description: A syllogism inference from two biconditionals. (Contributed by NM, 12-Mar-1993)

	Ref	Expression
Hypotheses	bitr4di.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
	bitr4di.2	⊢ ( 𝜃 ↔ 𝜒 )
Assertion	bitr4di	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜃 ) )

Proof

Step	Hyp	Ref	Expression
1		bitr4di.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
2		bitr4di.2	⊢ ( 𝜃 ↔ 𝜒 )
3	2	bicomi	⊢ ( 𝜒 ↔ 𝜃 )
4	1 3	bitrdi	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜃 ) )