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	$$⊢\phi \leftrightarrow \psi$$
	syl7bi.2	$$⊢\chi \to \left(\theta \to \left(\psi \to \tau \right)\right)$$
Assertion	syl7bi	$$⊢\chi \to \left(\theta \to \left(\phi \to \tau \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		syl7bi.1	$$⊢\phi \leftrightarrow \psi$$
2		syl7bi.2	$$⊢\chi \to \left(\theta \to \left(\psi \to \tau \right)\right)$$
3	1	biimpi	$$⊢\phi \to \psi$$
4	3 2	syl7	$$⊢\chi \to \left(\theta \to \left(\phi \to \tau \right)\right)$$