Theorem e33

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

	Ref	Expression
Hypotheses	e33.1	$$⊢\left(\phi ,\psi ,\chi \to \theta \right)$$
	e33.2	$$⊢\left(\phi ,\psi ,\chi \to \tau \right)$$
	e33.3	$$⊢\theta \to \left(\tau \to \eta \right)$$
Assertion	e33	$$⊢\left(\phi ,\psi ,\chi \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		e33.1	$$⊢\left(\phi ,\psi ,\chi \to \theta \right)$$
2		e33.2	$$⊢\left(\phi ,\psi ,\chi \to \tau \right)$$
3		e33.3	$$⊢\theta \to \left(\tau \to \eta \right)$$
4	3	a1i	$$⊢\theta \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
5	1 1 2 4	e333	$$⊢\left(\phi ,\psi ,\chi \to \eta \right)$$