Theorem e200

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

	Ref	Expression
Hypotheses	e200.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
	e200.2	$$⊢\theta$$
	e200.3	$$⊢\tau$$
	e200.4	$$⊢\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
Assertion	e200	$$⊢\left(\phi ,\psi \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		e200.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
2		e200.2	$$⊢\theta$$
3		e200.3	$$⊢\tau$$
4		e200.4	$$⊢\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
5	2	vd02	$$⊢\left(\phi ,\psi \to \theta \right)$$
6	3	vd02	$$⊢\left(\phi ,\psi \to \tau \right)$$
7	1 5 6 4	e222	$$⊢\left(\phi ,\psi \to \eta \right)$$