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| Mirrors > Home > ILE Home > Th. List > df-ple | GIF version | ||
| Description: Define "less than or equal to" ordering extractor for posets and related structures. We use ;10 for the index to avoid conflict with 1 through 9 used for other purposes. (Contributed by NM, 4-Sep-2011.) (Revised by Mario Carneiro, 14-Aug-2015.) (Revised by AV, 9-Sep-2021.) | 
| Ref | Expression | 
|---|---|
| df-ple | ⊢ le = Slot ;10 | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | cple 12762 | . 2 class le | |
| 2 | c1 7880 | . . . 4 class 1 | |
| 3 | cc0 7879 | . . . 4 class 0 | |
| 4 | 2, 3 | cdc 9457 | . . 3 class ;10 | 
| 5 | 4 | cslot 12677 | . 2 class Slot ;10 | 
| 6 | 1, 5 | wceq 1364 | 1 wff le = Slot ;10 | 
| Colors of variables: wff set class | 
| This definition is referenced by: plendx 12877 pleid 12878 pleslid 12879 | 
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