Theorem e022

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

	Ref	Expression
Hypotheses	e022.1	$$⊢\phi$$
	e022.2	$$⊢\left(\psi ,\chi \to \theta \right)$$
	e022.3	$$⊢\left(\psi ,\chi \to \tau \right)$$
	e022.4	$$⊢\phi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
Assertion	e022	$$⊢\left(\psi ,\chi \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		e022.1	$$⊢\phi$$
2		e022.2	$$⊢\left(\psi ,\chi \to \theta \right)$$
3		e022.3	$$⊢\left(\psi ,\chi \to \tau \right)$$
4		e022.4	$$⊢\phi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
5	1	vd02	$$⊢\left(\psi ,\chi \to \phi \right)$$
6	5 2 3 4	e222	$$⊢\left(\psi ,\chi \to \eta \right)$$