Theorem e000

Description: A virtual deduction elimination rule. The non-virtual deduction form of e000 is the virtual deduction form. (Contributed by Alan Sare, 14-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e000.1	$$⊢\phi$$
	e000.2	$$⊢\psi$$
	e000.3	$$⊢\chi$$
	e000.4	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
Assertion	e000	$$⊢\theta$$

Proof

Step	Hyp	Ref	Expression
1		e000.1	$$⊢\phi$$
2		e000.2	$$⊢\psi$$
3		e000.3	$$⊢\chi$$
4		e000.4	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
5	1 2 4	mp2	$$⊢\chi \to \theta$$
6	3 5	ax-mp	$$⊢\theta$$