Theorem e23an

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

	Ref	Expression
Hypotheses	e23an.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
	e23an.2	$$⊢\left(\phi ,\psi ,\theta \to \tau \right)$$
	e23an.3	$$⊢\left(\chi \wedge \tau \right)\to \eta$$
Assertion	e23an	$$⊢\left(\phi ,\psi ,\theta \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		e23an.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
2		e23an.2	$$⊢\left(\phi ,\psi ,\theta \to \tau \right)$$
3		e23an.3	$$⊢\left(\chi \wedge \tau \right)\to \eta$$
4	3	ex	$$⊢\chi \to \left(\tau \to \eta \right)$$
5	1 2 4	e23	$$⊢\left(\phi ,\psi ,\theta \to \eta \right)$$