Theorem e110

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

	Ref	Expression
Hypotheses	e110.1	$$⊢\left(\phi \to \psi \right)$$
	e110.2	$$⊢\left(\phi \to \chi \right)$$
	e110.3	$$⊢\theta$$
	e110.4	$$⊢\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)$$
Assertion	e110	$$⊢\left(\phi \to \tau \right)$$

Proof

Step	Hyp	Ref	Expression
1		e110.1	$$⊢\left(\phi \to \psi \right)$$
2		e110.2	$$⊢\left(\phi \to \chi \right)$$
3		e110.3	$$⊢\theta$$
4		e110.4	$$⊢\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)$$
5	3	vd01	$$⊢\left(\phi \to \theta \right)$$
6	1 2 5 4	e111	$$⊢\left(\phi \to \tau \right)$$