Description: A finite set has a minimum under a total order. (Contributed by AV, 6-Oct-2020)
Ref | Expression | ||
---|---|---|---|
Assertion | fiming | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fimin2g | |
|
2 | nesym | |
|
3 | 2 | imbi1i | |
4 | pm4.64 | |
|
5 | 3 4 | bitri | |
6 | sotric | |
|
7 | 6 | ancom2s | |
8 | 7 | con2bid | |
9 | 5 8 | bitrid | |
10 | 9 | anassrs | |
11 | 10 | ralbidva | |
12 | 11 | rexbidva | |
13 | 12 | 3ad2ant1 | |
14 | 1 13 | mpbird | |