Theorem e03

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e03.1	$$⊢\phi$$
	e03.2	$$⊢\left(\psi ,\chi ,\theta \to \tau \right)$$
	e03.3	$$⊢\phi \to \left(\tau \to \eta \right)$$
Assertion	e03	$$⊢\left(\psi ,\chi ,\theta \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		e03.1	$$⊢\phi$$
2		e03.2	$$⊢\left(\psi ,\chi ,\theta \to \tau \right)$$
3		e03.3	$$⊢\phi \to \left(\tau \to \eta \right)$$
4	1	vd03	$$⊢\left(\psi ,\chi ,\theta \to \phi \right)$$
5	4 2 3	e33	$$⊢\left(\psi ,\chi ,\theta \to \eta \right)$$