Theorem ee13

Description: e13 without virtual deduction connectives. Special theorem needed for the Virtual Deduction translation tool. (Contributed by Alan Sare, 28-Oct-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee13.1	$$⊢\phi \to \psi$$
	ee13.2	$$⊢\phi \to \left(\chi \to \left(\theta \to \tau \right)\right)$$
	ee13.3	$$⊢\psi \to \left(\tau \to \eta \right)$$
Assertion	ee13	$$⊢\phi \to \left(\chi \to \left(\theta \to \eta \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		ee13.1	$$⊢\phi \to \psi$$
2		ee13.2	$$⊢\phi \to \left(\chi \to \left(\theta \to \tau \right)\right)$$
3		ee13.3	$$⊢\psi \to \left(\tau \to \eta \right)$$
4	1 3	syl	$$⊢\phi \to \left(\tau \to \eta \right)$$
5	2 4	syl6d	$$⊢\phi \to \left(\chi \to \left(\theta \to \eta \right)\right)$$