Description: An unordered pair is dominated by ordinal two. (Contributed by RP, 29-Oct-2023)
Ref | Expression | ||
---|---|---|---|
Assertion | pr2dom | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-pr | |
|
2 | snex | |
|
3 | snex | |
|
4 | undjudom | |
|
5 | 2 3 4 | mp2an | |
6 | sn1dom | |
|
7 | djudom1 | |
|
8 | 6 3 7 | mp2an | |
9 | sn1dom | |
|
10 | 1on | |
|
11 | djudom2 | |
|
12 | 9 10 11 | mp2an | |
13 | domtr | |
|
14 | 8 12 13 | mp2an | |
15 | dju1p1e2 | |
|
16 | domentr | |
|
17 | 14 15 16 | mp2an | |
18 | domtr | |
|
19 | 5 17 18 | mp2an | |
20 | 1 19 | eqbrtri | |