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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-bj-tag | Structured version Visualization version GIF version |
Description: Definition of the tagged copy of a class, that is, the adjunction to (an isomorph of) 𝐴 of a disjoint element (here, the empty set). Remark: this could be used for the one-point compactification of a topological space. (Contributed by BJ, 6-Oct-2018.) |
Ref | Expression |
---|---|
df-bj-tag | ⊢ tag 𝐴 = (sngl 𝐴 ∪ {∅}) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 class 𝐴 | |
2 | 1 | bj-ctag 34787 | . 2 class tag 𝐴 |
3 | 1 | bj-csngl 34778 | . . 3 class sngl 𝐴 |
4 | c0 4211 | . . . 4 class ∅ | |
5 | 4 | csn 4516 | . . 3 class {∅} |
6 | 3, 5 | cun 3841 | . 2 class (sngl 𝐴 ∪ {∅}) |
7 | 2, 6 | wceq 1542 | 1 wff tag 𝐴 = (sngl 𝐴 ∪ {∅}) |
Colors of variables: wff setvar class |
This definition is referenced by: bj-tageq 34789 bj-eltag 34790 bj-0eltag 34791 bj-tagss 34793 bj-snglsstag 34794 bj-sngltag 34796 bj-tagex 34800 |
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