Theorem e31

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

	Ref	Expression
Hypotheses	e31.1	$$⊢\left(\phi ,\psi ,\chi \to \theta \right)$$
	e31.2	$$⊢\left(\phi \to \tau \right)$$
	e31.3	$$⊢\theta \to \left(\tau \to \eta \right)$$
Assertion	e31	$$⊢\left(\phi ,\psi ,\chi \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		e31.1	$$⊢\left(\phi ,\psi ,\chi \to \theta \right)$$
2		e31.2	$$⊢\left(\phi \to \tau \right)$$
3		e31.3	$$⊢\theta \to \left(\tau \to \eta \right)$$
4	2	vd13	$$⊢\left(\phi ,\psi ,\chi \to \tau \right)$$
5	1 4 3	e33	$$⊢\left(\phi ,\psi ,\chi \to \eta \right)$$