Theorem syl7bi

Description: A mixed syllogism inference from a doubly nested implication and a biconditional. (Contributed by NM, 14-May-1993)

	Ref	Expression
Hypotheses	syl7bi.1	⊢ ( 𝜑 ↔ 𝜓 )
	syl7bi.2	⊢ ( 𝜒 → ( 𝜃 → ( 𝜓 → 𝜏 ) ) )
Assertion	syl7bi	⊢ ( 𝜒 → ( 𝜃 → ( 𝜑 → 𝜏 ) ) )

Proof

Step	Hyp	Ref	Expression
1		syl7bi.1	⊢ ( 𝜑 ↔ 𝜓 )
2		syl7bi.2	⊢ ( 𝜒 → ( 𝜃 → ( 𝜓 → 𝜏 ) ) )
3	1	biimpi	⊢ ( 𝜑 → 𝜓 )
4	3 2	syl7	⊢ ( 𝜒 → ( 𝜃 → ( 𝜑 → 𝜏 ) ) )