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| Mirrors > Home > MPE Home > Th. List > df-ima | Structured version Visualization version GIF version | ||
| Description: Define the image of a class (as restricted by another class). Definition 6.6(2) of [TakeutiZaring] p. 24. For example, (𝐹 = {〈2, 6〉, 〈3, 9〉} ∧ 𝐵 = {1, 2}) → (𝐹 “ 𝐵) = {6} (ex-ima 30461). Contrast with restriction (df-res 5697) and range (df-rn 5696). For an alternate definition, see dfima2 6080. (Contributed by NM, 2-Aug-1994.) |
| Ref | Expression |
|---|---|
| df-ima | ⊢ (𝐴 “ 𝐵) = ran (𝐴 ↾ 𝐵) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cA | . . 3 class 𝐴 | |
| 2 | cB | . . 3 class 𝐵 | |
| 3 | 1, 2 | cima 5688 | . 2 class (𝐴 “ 𝐵) |
| 4 | 1, 2 | cres 5687 | . . 3 class (𝐴 ↾ 𝐵) |
| 5 | 4 | crn 5686 | . 2 class ran (𝐴 ↾ 𝐵) |
| 6 | 3, 5 | wceq 1540 | 1 wff (𝐴 “ 𝐵) = ran (𝐴 ↾ 𝐵) |
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