Theorem prtlem60

Description: Lemma for prter3 . (Contributed by Rodolfo Medina, 9-Oct-2010)

	Ref	Expression
Hypotheses	prtlem60.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
	prtlem60.2	$$⊢\psi \to \left(\theta \to \tau \right)$$
Assertion	prtlem60	$$⊢\phi \to \left(\psi \to \left(\chi \to \tau \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		prtlem60.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
2		prtlem60.2	$$⊢\psi \to \left(\theta \to \tau \right)$$
3	2	a1i	$$⊢\phi \to \left(\psi \to \left(\theta \to \tau \right)\right)$$
4	1 3	syldd	$$⊢\phi \to \left(\psi \to \left(\chi \to \tau \right)\right)$$