Theorem el0321old

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2015) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	el0321old.1	$$⊢\phi$$
	el0321old.2	$$⊢\left(\left(\psi ,\chi ,\theta \right)\to \tau \right)$$
	el0321old.3	$$⊢\left(\phi \wedge \tau \right)\to \eta$$
Assertion	el0321old	$$⊢\left(\left(\psi ,\chi ,\theta \right)\to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		el0321old.1	$$⊢\phi$$
2		el0321old.2	$$⊢\left(\left(\psi ,\chi ,\theta \right)\to \tau \right)$$
3		el0321old.3	$$⊢\left(\phi \wedge \tau \right)\to \eta$$
4	2	dfvd3ani	$$⊢\left(\psi \wedge \chi \wedge \theta \right)\to \tau$$
5	1 4 3	eel0321old	$$⊢\left(\psi \wedge \chi \wedge \theta \right)\to \eta$$
6	5	dfvd3anir	$$⊢\left(\left(\psi ,\chi ,\theta \right)\to \eta \right)$$