Metamath Proof Explorer


Definition df-ple

Description: Define "less than or equal to" ordering extractor for posets and related structures. (Contributed by NM, 4-Sep-2011) (Revised by Mario Carneiro, 14-Aug-2015) (Revised by AV, 9-Sep-2021) Use its index-independent form pleid instead. (New usage is discouraged.)

Ref Expression
Assertion df-ple le = Slot 1 0

Detailed syntax breakdown

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