Theorem e100

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

	Ref	Expression
Hypotheses	e100.1	$$⊢\left(\phi \to \psi \right)$$
	e100.2	$$⊢\chi$$
	e100.3	$$⊢\theta$$
	e100.4	$$⊢\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)$$
Assertion	e100	$$⊢\left(\phi \to \tau \right)$$

Proof

Step	Hyp	Ref	Expression
1		e100.1	$$⊢\left(\phi \to \psi \right)$$
2		e100.2	$$⊢\chi$$
3		e100.3	$$⊢\theta$$
4		e100.4	$$⊢\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)$$
5	2	vd01	$$⊢\left(\phi \to \chi \right)$$
6	3	vd01	$$⊢\left(\phi \to \theta \right)$$
7	1 5 6 4	e111	$$⊢\left(\phi \to \tau \right)$$