Theorem e10

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

	Ref	Expression
Hypotheses	e10.1	$$⊢\left(\phi \to \psi \right)$$
	e10.2	$$⊢\chi$$
	e10.3	$$⊢\psi \to \left(\chi \to \theta \right)$$
Assertion	e10	$$⊢\left(\phi \to \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		e10.1	$$⊢\left(\phi \to \psi \right)$$
2		e10.2	$$⊢\chi$$
3		e10.3	$$⊢\psi \to \left(\chi \to \theta \right)$$
4	2	vd01	$$⊢\left(\phi \to \chi \right)$$
5	1 4 3	e11	$$⊢\left(\phi \to \theta \right)$$