Theorem ee010

Description: e010 without virtual deductions. (Contributed by Alan Sare, 23-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee010.1	$$⊢\phi$$
	ee010.2	$$⊢\psi \to \chi$$
	ee010.3	$$⊢\theta$$
	ee010.4	$$⊢\phi \to \left(\chi \to \left(\theta \to \tau \right)\right)$$
Assertion	ee010	$$⊢\psi \to \tau$$

Proof

Step	Hyp	Ref	Expression
1		ee010.1	$$⊢\phi$$
2		ee010.2	$$⊢\psi \to \chi$$
3		ee010.3	$$⊢\theta$$
4		ee010.4	$$⊢\phi \to \left(\chi \to \left(\theta \to \tau \right)\right)$$
5	1	a1i	$$⊢\psi \to \phi$$
6	3	a1i	$$⊢\psi \to \theta$$
7	5 2 6 4	syl3c	$$⊢\psi \to \tau$$