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Mirrors > Home > MPE Home > Th. List > df-cnrm | Structured version Visualization version GIF version |
Description: Define completely normal spaces. A space is completely normal if all its subspaces are normal. (Contributed by Mario Carneiro, 26-Aug-2015.) |
Ref | Expression |
---|---|
df-cnrm | ⊢ CNrm = {𝑗 ∈ Top ∣ ∀𝑥 ∈ 𝒫 ∪ 𝑗(𝑗 ↾t 𝑥) ∈ Nrm} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ccnrm 22460 | . 2 class CNrm | |
2 | vj | . . . . . . 7 setvar 𝑗 | |
3 | 2 | cv 1541 | . . . . . 6 class 𝑗 |
4 | vx | . . . . . . 7 setvar 𝑥 | |
5 | 4 | cv 1541 | . . . . . 6 class 𝑥 |
6 | crest 17129 | . . . . . 6 class ↾t | |
7 | 3, 5, 6 | co 7271 | . . . . 5 class (𝑗 ↾t 𝑥) |
8 | cnrm 22459 | . . . . 5 class Nrm | |
9 | 7, 8 | wcel 2110 | . . . 4 wff (𝑗 ↾t 𝑥) ∈ Nrm |
10 | 3 | cuni 4845 | . . . . 5 class ∪ 𝑗 |
11 | 10 | cpw 4539 | . . . 4 class 𝒫 ∪ 𝑗 |
12 | 9, 4, 11 | wral 3066 | . . 3 wff ∀𝑥 ∈ 𝒫 ∪ 𝑗(𝑗 ↾t 𝑥) ∈ Nrm |
13 | ctop 22040 | . . 3 class Top | |
14 | 12, 2, 13 | crab 3070 | . 2 class {𝑗 ∈ Top ∣ ∀𝑥 ∈ 𝒫 ∪ 𝑗(𝑗 ↾t 𝑥) ∈ Nrm} |
15 | 1, 14 | wceq 1542 | 1 wff CNrm = {𝑗 ∈ Top ∣ ∀𝑥 ∈ 𝒫 ∪ 𝑗(𝑗 ↾t 𝑥) ∈ Nrm} |
Colors of variables: wff setvar class |
This definition is referenced by: iscnrm 22472 |
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