Theorem e13

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e13.1	$$⊢\left(\phi \to \psi \right)$$
	e13.2	$$⊢\left(\phi ,\chi ,\theta \to \tau \right)$$
	e13.3	$$⊢\psi \to \left(\tau \to \eta \right)$$
Assertion	e13	$$⊢\left(\phi ,\chi ,\theta \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		e13.1	$$⊢\left(\phi \to \psi \right)$$
2		e13.2	$$⊢\left(\phi ,\chi ,\theta \to \tau \right)$$
3		e13.3	$$⊢\psi \to \left(\tau \to \eta \right)$$
4	1	vd13	$$⊢\left(\phi ,\chi ,\theta \to \psi \right)$$
5	4 2 3	e33	$$⊢\left(\phi ,\chi ,\theta \to \eta \right)$$