Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > df-ple | Structured version Visualization version 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 16809 | . 2 class le | |
2 | c1 10730 | . . . 4 class 1 | |
3 | cc0 10729 | . . . 4 class 0 | |
4 | 2, 3 | cdc 12293 | . . 3 class ;10 |
5 | 4 | cslot 16734 | . 2 class Slot ;10 |
6 | 1, 5 | wceq 1543 | 1 wff le = Slot ;10 |
Colors of variables: wff setvar class |
This definition is referenced by: plendx 16893 pleid 16894 0posOLD 17829 isposix 17832 oppgle 30958 |
Copyright terms: Public domain | W3C validator |