Theorem sylbb1

Description: A mixed syllogism inference from two biconditionals. (Contributed by BJ, 21-Apr-2019)

	Ref	Expression
Hypotheses	sylbb1.1	⊢ ( 𝜑 ↔ 𝜓 )
	sylbb1.2	⊢ ( 𝜑 ↔ 𝜒 )
Assertion	sylbb1	⊢ ( 𝜓 → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		sylbb1.1	⊢ ( 𝜑 ↔ 𝜓 )
2		sylbb1.2	⊢ ( 𝜑 ↔ 𝜒 )
3	1	biimpri	⊢ ( 𝜓 → 𝜑 )
4	3 2	sylib	⊢ ( 𝜓 → 𝜒 )