Theorem syl5ib

Description: A mixed syllogism inference. (Contributed by NM, 12-Jan-1993)

	Ref	Expression
Hypotheses	syl5ib.1	$$⊢\phi \to \psi$$
	syl5ib.2	$$⊢\chi \to \left(\psi \leftrightarrow \theta \right)$$
Assertion	syl5ib	$$⊢\chi \to \left(\phi \to \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		syl5ib.1	$$⊢\phi \to \psi$$
2		syl5ib.2	$$⊢\chi \to \left(\psi \leftrightarrow \theta \right)$$
3	2	biimpd	$$⊢\chi \to \left(\psi \to \theta \right)$$
4	1 3	syl5	$$⊢\chi \to \left(\phi \to \theta \right)$$