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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 9005 and brsdom2 9134. Definition 3 of [Suppes] p. 97. (Contributed by NM, 31-Mar-1998.) |
Ref | Expression |
---|---|
df-sdom | ⊢ ≺ = ( ≼ ∖ ≈ ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csdm 8972 | . 2 class ≺ | |
2 | cdom 8971 | . . 3 class ≼ | |
3 | cen 8970 | . . 3 class ≈ | |
4 | 2, 3 | cdif 3943 | . 2 class ( ≼ ∖ ≈ ) |
5 | 1, 4 | wceq 1533 | 1 wff ≺ = ( ≼ ∖ ≈ ) |
Colors of variables: wff setvar class |
This definition is referenced by: relsdom 8980 brsdom 9005 dfdom2 9008 dfsdom2 9133 |
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