Metamath Proof Explorer


Definition df-ple

Description: Define "less than or equal to" ordering extractor for posets and related structures. We use ; 1 0 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
Assertion df-ple le = Slot 10

Detailed syntax breakdown

Step Hyp Ref Expression
0 cple class le
1 c1 class 1
2 cc0 class 0
3 1 2 cdc class 10
4 3 cslot class Slot 10
5 0 4 wceq wff le = Slot 10