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Mirrors > Home > ILE Home > Th. List > df-cnp | Unicode version |
Description: Define a function on two topologies whose value is the set of continuous mappings at a specified point in the first topology. Based on Theorem 7.2(g) of [Munkres] p. 107. (Contributed by NM, 17-Oct-2006.) |
Ref | Expression |
---|---|
df-cnp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ccnp 12727 | . 2 | |
2 | vj | . . 3 | |
3 | vk | . . 3 | |
4 | ctop 12536 | . . 3 | |
5 | vx | . . . 4 | |
6 | 2 | cv 1341 | . . . . 5 |
7 | 6 | cuni 3783 | . . . 4 |
8 | 5 | cv 1341 | . . . . . . . . 9 |
9 | vf | . . . . . . . . . 10 | |
10 | 9 | cv 1341 | . . . . . . . . 9 |
11 | 8, 10 | cfv 5182 | . . . . . . . 8 |
12 | vy | . . . . . . . . 9 | |
13 | 12 | cv 1341 | . . . . . . . 8 |
14 | 11, 13 | wcel 2135 | . . . . . . 7 |
15 | vg | . . . . . . . . . 10 | |
16 | 5, 15 | wel 2136 | . . . . . . . . 9 |
17 | 15 | cv 1341 | . . . . . . . . . . 11 |
18 | 10, 17 | cima 4601 | . . . . . . . . . 10 |
19 | 18, 13 | wss 3111 | . . . . . . . . 9 |
20 | 16, 19 | wa 103 | . . . . . . . 8 |
21 | 20, 15, 6 | wrex 2443 | . . . . . . 7 |
22 | 14, 21 | wi 4 | . . . . . 6 |
23 | 3 | cv 1341 | . . . . . 6 |
24 | 22, 12, 23 | wral 2442 | . . . . 5 |
25 | 23 | cuni 3783 | . . . . . 6 |
26 | cmap 6605 | . . . . . 6 | |
27 | 25, 7, 26 | co 5836 | . . . . 5 |
28 | 24, 9, 27 | crab 2446 | . . . 4 |
29 | 5, 7, 28 | cmpt 4037 | . . 3 |
30 | 2, 3, 4, 4, 29 | cmpo 5838 | . 2 |
31 | 1, 30 | wceq 1342 | 1 |
Colors of variables: wff set class |
This definition is referenced by: cnpfval 12736 cnprcl2k 12747 |
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