| Mathbox for Peter Mazsa |
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| Mirrors > Home > MPE Home > Th. List > Mathboxes > df-membparts | Structured version Visualization version GIF version | ||
| Description: Define the class of member partition relations on their domain quotients. (Contributed by Peter Mazsa, 26-Jun-2021.) |
| Ref | Expression |
|---|---|
| df-membparts | ⊢ MembParts = {𝑎 ∣ (◡ E ↾ 𝑎) Parts 𝑎} |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cmembparts 38222 | . 2 class MembParts | |
| 2 | cep 5583 | . . . . . 6 class E | |
| 3 | 2 | ccnv 5684 | . . . . 5 class ◡ E |
| 4 | va | . . . . . 6 setvar 𝑎 | |
| 5 | 4 | cv 1539 | . . . . 5 class 𝑎 |
| 6 | 3, 5 | cres 5687 | . . . 4 class (◡ E ↾ 𝑎) |
| 7 | cparts 38220 | . . . 4 class Parts | |
| 8 | 6, 5, 7 | wbr 5143 | . . 3 wff (◡ E ↾ 𝑎) Parts 𝑎 |
| 9 | 8, 4 | cab 2714 | . 2 class {𝑎 ∣ (◡ E ↾ 𝑎) Parts 𝑎} |
| 10 | 1, 9 | wceq 1540 | 1 wff MembParts = {𝑎 ∣ (◡ E ↾ 𝑎) Parts 𝑎} |
| Colors of variables: wff setvar class |
| This definition is referenced by: mpets 38843 |
| Copyright terms: Public domain | W3C validator |