Theorem e001

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e001.1	$$⊢\phi$$
	e001.2	$$⊢\psi$$
	e001.3	$$⊢\left(\chi \to \theta \right)$$
	e001.4	$$⊢\phi \to \left(\psi \to \left(\theta \to \tau \right)\right)$$
Assertion	e001	$$⊢\left(\chi \to \tau \right)$$

Proof

Step	Hyp	Ref	Expression
1		e001.1	$$⊢\phi$$
2		e001.2	$$⊢\psi$$
3		e001.3	$$⊢\left(\chi \to \theta \right)$$
4		e001.4	$$⊢\phi \to \left(\psi \to \left(\theta \to \tau \right)\right)$$
5	1	vd01	$$⊢\left(\chi \to \phi \right)$$
6	2	vd01	$$⊢\left(\chi \to \psi \right)$$
7	5 6 3 4	e111	$$⊢\left(\chi \to \tau \right)$$