Theorem sylbb

Description: A mixed syllogism inference from two biconditionals. (Contributed by BJ, 30-Mar-2019)

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

Proof

Step	Hyp	Ref	Expression
1		sylbb.1	⊢ ( 𝜑 ↔ 𝜓 )
2		sylbb.2	⊢ ( 𝜓 ↔ 𝜒 )
3	2	biimpi	⊢ ( 𝜓 → 𝜒 )
4	1 3	sylbi	⊢ ( 𝜑 → 𝜒 )