Theorem syl9

Description: A nested syllogism inference with different antecedents. (Contributed by NM, 13-May-1993) (Proof shortened by Josh Purinton, 29-Dec-2000)

	Ref	Expression
Hypotheses	syl9.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
	syl9.2	$$⊢\theta \to \left(\chi \to \tau \right)$$
Assertion	syl9	$$⊢\phi \to \left(\theta \to \left(\psi \to \tau \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		syl9.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		syl9.2	$$⊢\theta \to \left(\chi \to \tau \right)$$
3	2	a1i	$$⊢\phi \to \left(\theta \to \left(\chi \to \tau \right)\right)$$
4	1 3	syl5d	$$⊢\phi \to \left(\theta \to \left(\psi \to \tau \right)\right)$$