Theorem e210

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

	Ref	Expression
Hypotheses	e210.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
	e210.2	$$⊢\left(\phi \to \theta \right)$$
	e210.3	$$⊢\tau$$
	e210.4	$$⊢\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
Assertion	e210	$$⊢\left(\phi ,\psi \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		e210.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
2		e210.2	$$⊢\left(\phi \to \theta \right)$$
3		e210.3	$$⊢\tau$$
4		e210.4	$$⊢\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
5	3	vd01	$$⊢\left(\phi \to \tau \right)$$
6	1 2 5 4	e211	$$⊢\left(\phi ,\psi \to \eta \right)$$