Theorem e020

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

	Ref	Expression
Hypotheses	e020.1	$$⊢\phi$$
	e020.2	$$⊢\left(\psi ,\chi \to \theta \right)$$
	e020.3	$$⊢\tau$$
	e020.4	$$⊢\phi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
Assertion	e020	$$⊢\left(\psi ,\chi \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		e020.1	$$⊢\phi$$
2		e020.2	$$⊢\left(\psi ,\chi \to \theta \right)$$
3		e020.3	$$⊢\tau$$
4		e020.4	$$⊢\phi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
5	1	vd02	$$⊢\left(\psi ,\chi \to \phi \right)$$
6	3	vd02	$$⊢\left(\psi ,\chi \to \tau \right)$$
7	5 2 6 4	e222	$$⊢\left(\psi ,\chi \to \eta \right)$$