Theorem e010

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

	Ref	Expression
Hypotheses	e010.1	$$⊢\phi$$
	e010.2	$$⊢\left(\psi \to \chi \right)$$
	e010.3	$$⊢\theta$$
	e010.4	$$⊢\phi \to \left(\chi \to \left(\theta \to \tau \right)\right)$$
Assertion	e010	$$⊢\left(\psi \to \tau \right)$$

Proof

Step	Hyp	Ref	Expression
1		e010.1	$$⊢\phi$$
2		e010.2	$$⊢\left(\psi \to \chi \right)$$
3		e010.3	$$⊢\theta$$
4		e010.4	$$⊢\phi \to \left(\chi \to \left(\theta \to \tau \right)\right)$$
5	1	vd01	$$⊢\left(\psi \to \phi \right)$$
6	3	vd01	$$⊢\left(\psi \to \theta \right)$$
7	5 2 6 4	e111	$$⊢\left(\psi \to \tau \right)$$