Theorem syl5ibr

Description: A mixed syllogism inference. (Contributed by NM, 3-Apr-1994)

	Ref	Expression
Hypotheses	syl5ibr.1	$$⊢\phi \to \theta$$
	syl5ibr.2	$$⊢\chi \to \left(\psi \leftrightarrow \theta \right)$$
Assertion	syl5ibr	$$⊢\chi \to \left(\phi \to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		syl5ibr.1	$$⊢\phi \to \theta$$
2		syl5ibr.2	$$⊢\chi \to \left(\psi \leftrightarrow \theta \right)$$
3	2	bicomd	$$⊢\chi \to \left(\theta \leftrightarrow \psi \right)$$
4	1 3	syl5ib	$$⊢\chi \to \left(\phi \to \psi \right)$$