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Description: Define the structure component index extractor. See Theorem ndxarg to understand its purpose. The restriction to NN 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 CC or (if we revise all structure component definitions such as df-base ) another set such as the set of finite ordinals _om ( df-om ). (Contributed by NM, 4-Sep-2011)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | df-ndx | ⊢ ndx = ( I ↾ ℕ ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 0 | cnx | ⊢ ndx | |
| 1 | cid | ⊢ I | |
| 2 | cn | ⊢ ℕ | |
| 3 | 1 2 | cres | ⊢ ( I ↾ ℕ ) |
| 4 | 0 3 | wceq | ⊢ ndx = ( I ↾ ℕ ) |