Theorem syli

Description: Syllogism inference with common nested antecedent. (Contributed by NM, 4-Nov-2004)

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

Proof

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