Theorem syl6ib

Description: A mixed syllogism inference from a nested implication and a biconditional. (Contributed by NM, 21-Jun-1993)

	Ref	Expression
Hypotheses	syl6ib.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
	syl6ib.2	$$⊢\chi \leftrightarrow \theta$$
Assertion	syl6ib	$$⊢\phi \to \left(\psi \to \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		syl6ib.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		syl6ib.2	$$⊢\chi \leftrightarrow \theta$$
3	2	biimpi	$$⊢\chi \to \theta$$
4	1 3	syl6	$$⊢\phi \to \left(\psi \to \theta \right)$$