Theorem e220

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

	Ref	Expression
Hypotheses	e220.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
	e220.2	$$⊢\left(\phi ,\psi \to \theta \right)$$
	e220.3	$$⊢\tau$$
	e220.4	$$⊢\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
Assertion	e220	$$⊢\left(\phi ,\psi \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		e220.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
2		e220.2	$$⊢\left(\phi ,\psi \to \theta \right)$$
3		e220.3	$$⊢\tau$$
4		e220.4	$$⊢\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
5	3	vd02	$$⊢\left(\phi ,\psi \to \tau \right)$$
6	1 2 5 4	e222	$$⊢\left(\phi ,\psi \to \eta \right)$$