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| Mirrors > Home > MPE Home > Th. List > df-sdom | Structured version Visualization version GIF version | ||
| Description: Define the strict dominance relation. Alternate possible definitions are derived as brsdom 9015 and brsdom2 9137. Definition 3 of [Suppes] p. 97. (Contributed by NM, 31-Mar-1998.) |
| Ref | Expression |
|---|---|
| df-sdom | ⊢ ≺ = ( ≼ ∖ ≈ ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | csdm 8984 | . 2 class ≺ | |
| 2 | cdom 8983 | . . 3 class ≼ | |
| 3 | cen 8982 | . . 3 class ≈ | |
| 4 | 2, 3 | cdif 3948 | . 2 class ( ≼ ∖ ≈ ) |
| 5 | 1, 4 | wceq 1540 | 1 wff ≺ = ( ≼ ∖ ≈ ) |
| Colors of variables: wff setvar class |
| This definition is referenced by: relsdom 8992 brsdom 9015 dfdom2 9018 dfsdom2 9136 |
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