Theorem sylbir

Description: A mixed syllogism inference from a biconditional and an implication. (Contributed by NM, 3-Jan-1993)

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

Proof

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