Theorem e102

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

	Ref	Expression
Hypotheses	e102.1	$$⊢\left(\phi \to \psi \right)$$
	e102.2	$$⊢\chi$$
	e102.3	$$⊢\left(\phi ,\theta \to \tau \right)$$
	e102.4	$$⊢\psi \to \left(\chi \to \left(\tau \to \eta \right)\right)$$
Assertion	e102	$$⊢\left(\phi ,\theta \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		e102.1	$$⊢\left(\phi \to \psi \right)$$
2		e102.2	$$⊢\chi$$
3		e102.3	$$⊢\left(\phi ,\theta \to \tau \right)$$
4		e102.4	$$⊢\psi \to \left(\chi \to \left(\tau \to \eta \right)\right)$$
5	2	vd01	$$⊢\left(\phi \to \chi \right)$$
6	1 5 3 4	e112	$$⊢\left(\phi ,\theta \to \eta \right)$$