Theorem e002

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

	Ref	Expression
Hypotheses	e002.1	$$⊢\phi$$
	e002.2	$$⊢\psi$$
	e002.3	$$⊢\left(\chi ,\theta \to \tau \right)$$
	e002.4	$$⊢\phi \to \left(\psi \to \left(\tau \to \eta \right)\right)$$
Assertion	e002	$$⊢\left(\chi ,\theta \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		e002.1	$$⊢\phi$$
2		e002.2	$$⊢\psi$$
3		e002.3	$$⊢\left(\chi ,\theta \to \tau \right)$$
4		e002.4	$$⊢\phi \to \left(\psi \to \left(\tau \to \eta \right)\right)$$
5	1	vd02	$$⊢\left(\chi ,\theta \to \phi \right)$$
6	2	vd02	$$⊢\left(\chi ,\theta \to \psi \right)$$
7	5 6 3 4	e222	$$⊢\left(\chi ,\theta \to \eta \right)$$