Theorem e012

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

	Ref	Expression
Hypotheses	e012.1	$$⊢\phi$$
	e012.2	$$⊢\left(\psi \to \chi \right)$$
	e012.3	$$⊢\left(\psi ,\theta \to \tau \right)$$
	e012.4	$$⊢\phi \to \left(\chi \to \left(\tau \to \eta \right)\right)$$
Assertion	e012	$$⊢\left(\psi ,\theta \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		e012.1	$$⊢\phi$$
2		e012.2	$$⊢\left(\psi \to \chi \right)$$
3		e012.3	$$⊢\left(\psi ,\theta \to \tau \right)$$
4		e012.4	$$⊢\phi \to \left(\chi \to \left(\tau \to \eta \right)\right)$$
5	1	vd01	$$⊢\left(\psi \to \phi \right)$$
6	5 2 3 4	e112	$$⊢\left(\psi ,\theta \to \eta \right)$$