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Mirrors > Home > ILE Home > Th. List > df-ndx | GIF version |
Description: Define the structure component index extractor. See theorem ndxarg 12012 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 11995) another set such as the set of finite ordinals ω (df-iom 4509). (Contributed by NM, 4-Sep-2011.) |
Ref | Expression |
---|---|
df-ndx | ⊢ ndx = ( I ↾ ℕ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnx 11986 | . 2 class ndx | |
2 | cid 4214 | . . 3 class I | |
3 | cn 8740 | . . 3 class ℕ | |
4 | 2, 3 | cres 4545 | . 2 class ( I ↾ ℕ) |
5 | 1, 4 | wceq 1332 | 1 wff ndx = ( I ↾ ℕ) |
Colors of variables: wff set class |
This definition is referenced by: ndxarg 12012 |
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