Theorem e201

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

	Ref	Expression
Hypotheses	e201.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
	e201.2	$$⊢\theta$$
	e201.3	$$⊢\left(\phi \to \tau \right)$$
	e201.4	$$⊢\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
Assertion	e201	$$⊢\left(\phi ,\psi \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		e201.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
2		e201.2	$$⊢\theta$$
3		e201.3	$$⊢\left(\phi \to \tau \right)$$
4		e201.4	$$⊢\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
5	2	vd01	$$⊢\left(\phi \to \theta \right)$$
6	1 5 3 4	e211	$$⊢\left(\phi ,\psi \to \eta \right)$$