Theorem 0nei

Description: The empty set is a neighborhood of itself. (Contributed by FL, 10-Dec-2006)

	Ref	Expression
Assertion	0nei	$$⊢J\in \mathrm{Top}\to \varnothing \in \mathrm{nei}\left(J\right)\left(\varnothing \right)$$

Proof

Step	Hyp	Ref	Expression
1		0opn	$$⊢J\in \mathrm{Top}\to \varnothing \in J$$
2		opnneiid	$$⊢J\in \mathrm{Top}\to \left(\varnothing \in \mathrm{nei}\left(J\right)\left(\varnothing \right)\leftrightarrow \varnothing \in J\right)$$
3	1 2	mpbird	$$⊢J\in \mathrm{Top}\to \varnothing \in \mathrm{nei}\left(J\right)\left(\varnothing \right)$$