Theorem e101

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

	Ref	Expression
Hypotheses	e101.1	$$⊢\left(\phi \to \psi \right)$$
	e101.2	$$⊢\chi$$
	e101.3	$$⊢\left(\phi \to \theta \right)$$
	e101.4	$$⊢\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)$$
Assertion	e101	$$⊢\left(\phi \to \tau \right)$$

Proof

Step	Hyp	Ref	Expression
1		e101.1	$$⊢\left(\phi \to \psi \right)$$
2		e101.2	$$⊢\chi$$
3		e101.3	$$⊢\left(\phi \to \theta \right)$$
4		e101.4	$$⊢\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)$$
5	2	vd01	$$⊢\left(\phi \to \chi \right)$$
6	1 5 3 4	e111	$$⊢\left(\phi \to \tau \right)$$