Theorem e01

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 25-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e01.1	$$⊢\phi$$
	e01.2	$$⊢\left(\psi \to \chi \right)$$
	e01.3	$$⊢\phi \to \left(\chi \to \theta \right)$$
Assertion	e01	$$⊢\left(\psi \to \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		e01.1	$$⊢\phi$$
2		e01.2	$$⊢\left(\psi \to \chi \right)$$
3		e01.3	$$⊢\phi \to \left(\chi \to \theta \right)$$
4	1	vd01	$$⊢\left(\psi \to \phi \right)$$
5	4 2 3	e11	$$⊢\left(\psi \to \theta \right)$$