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Mirrors > Home > MPE Home > Th. List > df-ndx | Structured version Visualization version GIF version |
Description: Define the structure component index extractor. See theorem ndxarg 16342 to understand its purpose. The restriction to ℕ ensures that ndx is a set. The restriction to some set is necessary since I is a proper class. In principle, we could have chosen ℂ or (if we revise all structure component definitions such as df-base 16323) another set such as the set of finite ordinals ω (df-om 7442). (Contributed by NM, 4-Sep-2011.) |
Ref | Expression |
---|---|
df-ndx | ⊢ ndx = ( I ↾ ℕ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnx 16314 | . 2 class ndx | |
2 | cid 5352 | . . 3 class I | |
3 | cn 11491 | . . 3 class ℕ | |
4 | 2, 3 | cres 5450 | . 2 class ( I ↾ ℕ) |
5 | 1, 4 | wceq 1522 | 1 wff ndx = ( I ↾ ℕ) |
Colors of variables: wff setvar class |
This definition is referenced by: wunndx 16338 ndxarg 16342 bj-ndxarg 33991 |
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