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| Mirrors > Home > MPE Home > Th. List > Mathboxes > df-disjss | Structured version Visualization version GIF version | ||
| Description: Define the class of all disjoint sets (but not necessarily disjoint relations, cf. df-disjs 38705). It is used only by df-disjs 38705. (Contributed by Peter Mazsa, 17-Jul-2021.) | 
| Ref | Expression | 
|---|---|
| df-disjss | ⊢ Disjss = {𝑥 ∣ ≀ ◡𝑥 ∈ CnvRefRels } | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | cdisjss 38214 | . 2 class Disjss | |
| 2 | vx | . . . . . . 7 setvar 𝑥 | |
| 3 | 2 | cv 1539 | . . . . . 6 class 𝑥 | 
| 4 | 3 | ccnv 5684 | . . . . 5 class ◡𝑥 | 
| 5 | 4 | ccoss 38182 | . . . 4 class ≀ ◡𝑥 | 
| 6 | ccnvrefrels 38190 | . . . 4 class CnvRefRels | |
| 7 | 5, 6 | wcel 2108 | . . 3 wff ≀ ◡𝑥 ∈ CnvRefRels | 
| 8 | 7, 2 | cab 2714 | . 2 class {𝑥 ∣ ≀ ◡𝑥 ∈ CnvRefRels } | 
| 9 | 1, 8 | wceq 1540 | 1 wff Disjss = {𝑥 ∣ ≀ ◡𝑥 ∈ CnvRefRels } | 
| Colors of variables: wff setvar class | 
| This definition is referenced by: dfdisjs 38709 | 
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