Theorem e23

Description: A virtual deduction elimination rule (see syl10 ). (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e23.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
	e23.2	$$⊢\left(\phi ,\psi ,\theta \to \tau \right)$$
	e23.3	$$⊢\chi \to \left(\tau \to \eta \right)$$
Assertion	e23	$$⊢\left(\phi ,\psi ,\theta \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		e23.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
2		e23.2	$$⊢\left(\phi ,\psi ,\theta \to \tau \right)$$
3		e23.3	$$⊢\chi \to \left(\tau \to \eta \right)$$
4	1	vd23	$$⊢\left(\phi ,\psi ,\theta \to \chi \right)$$
5	4 2 3	e33	$$⊢\left(\phi ,\psi ,\theta \to \eta \right)$$