Theorem e11

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

	Ref	Expression
Hypotheses	e11.1	$$⊢\left(\phi \to \psi \right)$$
	e11.2	$$⊢\left(\phi \to \chi \right)$$
	e11.3	$$⊢\psi \to \left(\chi \to \theta \right)$$
Assertion	e11	$$⊢\left(\phi \to \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		e11.1	$$⊢\left(\phi \to \psi \right)$$
2		e11.2	$$⊢\left(\phi \to \chi \right)$$
3		e11.3	$$⊢\psi \to \left(\chi \to \theta \right)$$
4	3	a1i	$$⊢\psi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
5	1 1 2 4	e111	$$⊢\left(\phi \to \theta \right)$$