Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > df-plt | Structured version Visualization version Unicode version |
Description: Define less-than ordering for posets and related structures. Unlike df-base 15863 and df-ple 15961, this is a derived component extractor and not an extensible structure component extractor that defines the poset. (Contributed by NM, 12-Oct-2011.) (Revised by Mario Carneiro, 8-Feb-2015.) |
Ref | Expression |
---|---|
df-plt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cplt 16941 | . 2 | |
2 | vp | . . 3 | |
3 | cvv 3200 | . . 3 | |
4 | 2 | cv 1482 | . . . . 5 |
5 | cple 15948 | . . . . 5 | |
6 | 4, 5 | cfv 5888 | . . . 4 |
7 | cid 5023 | . . . 4 | |
8 | 6, 7 | cdif 3571 | . . 3 |
9 | 2, 3, 8 | cmpt 4729 | . 2 |
10 | 1, 9 | wceq 1483 | 1 |
Colors of variables: wff setvar class |
This definition is referenced by: pltfval 16959 |
Copyright terms: Public domain | W3C validator |