Description: Given a neighborhood N of P , each subset of the neighborhood space containing this neighborhood is also a neighborhood of P . Axiom B of Seifert and Threlfall. (Contributed by RP, 5-Apr-2021)
Ref | Expression | ||
---|---|---|---|
Hypothesis | gneispace.x | |
|
Assertion | gneispb | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | gneispace.x | |
|
2 | 3simpb | |
|
3 | 2 | ad2antrr | |
4 | simpr | |
|
5 | simplr | |
|
6 | 5 | elpwid | |
7 | 1 | ssnei2 | |
8 | 3 4 6 7 | syl12anc | |
9 | 8 | exp31 | |
10 | 9 | ralrimiv | |