Theorem syl5ibcom

Description: A mixed syllogism inference. (Contributed by NM, 19-Jun-2007)

	Ref	Expression
Hypotheses	syl5ib.1	$$⊢\phi \to \psi$$
	syl5ib.2	$$⊢\chi \to \left(\psi \leftrightarrow \theta \right)$$
Assertion	syl5ibcom	$$⊢\phi \to \left(\chi \to \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		syl5ib.1	$$⊢\phi \to \psi$$
2		syl5ib.2	$$⊢\chi \to \left(\psi \leftrightarrow \theta \right)$$
3	1 2	syl5ib	$$⊢\chi \to \left(\phi \to \theta \right)$$
4	3	com12	$$⊢\phi \to \left(\chi \to \theta \right)$$