Theorem sylib

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

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

Proof

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