Theorem ee001

Description: e001 without virtual deductions. (Contributed by Alan Sare, 23-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee001.1	$$⊢\phi$$
	ee001.2	$$⊢\psi$$
	ee001.3	$$⊢\chi \to \theta$$
	ee001.4	$$⊢\phi \to \left(\psi \to \left(\theta \to \tau \right)\right)$$
Assertion	ee001	$$⊢\chi \to \tau$$

Proof

Step	Hyp	Ref	Expression
1		ee001.1	$$⊢\phi$$
2		ee001.2	$$⊢\psi$$
3		ee001.3	$$⊢\chi \to \theta$$
4		ee001.4	$$⊢\phi \to \left(\psi \to \left(\theta \to \tau \right)\right)$$
5	1	a1i	$$⊢\chi \to \phi$$
6	2	a1i	$$⊢\chi \to \psi$$
7	5 6 3 4	syl3c	$$⊢\chi \to \tau$$