Theorem e02

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 14-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e02.1	$$⊢\phi$$
	e02.2	$$⊢\left(\psi ,\chi \to \theta \right)$$
	e02.3	$$⊢\phi \to \left(\theta \to \tau \right)$$
Assertion	e02	$$⊢\left(\psi ,\chi \to \tau \right)$$

Proof

Step	Hyp	Ref	Expression
1		e02.1	$$⊢\phi$$
2		e02.2	$$⊢\left(\psi ,\chi \to \theta \right)$$
3		e02.3	$$⊢\phi \to \left(\theta \to \tau \right)$$
4	1	vd02	$$⊢\left(\psi ,\chi \to \phi \right)$$
5	4 2 3	e22	$$⊢\left(\psi ,\chi \to \tau \right)$$