Theorem syl9r

Description: A nested syllogism inference with different antecedents. (Contributed by NM, 14-May-1993)

	Ref	Expression
Hypotheses	syl9r.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
	syl9r.2	$$⊢\theta \to \left(\chi \to \tau \right)$$
Assertion	syl9r	$$⊢\theta \to \left(\phi \to \left(\psi \to \tau \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		syl9r.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		syl9r.2	$$⊢\theta \to \left(\chi \to \tau \right)$$
3	1 2	syl9	$$⊢\phi \to \left(\theta \to \left(\psi \to \tau \right)\right)$$
4	3	com12	$$⊢\theta \to \left(\phi \to \left(\psi \to \tau \right)\right)$$