Description: The union of a finite ordinal is a finite ordinal. (Contributed by Scott Fenton, 17-Oct-2024)
Ref | Expression | ||
---|---|---|---|
Assertion | nnuni | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nn0suc | |
|
2 | unieq | |
|
3 | uni0 | |
|
4 | 2 3 | eqtrdi | |
5 | peano1 | |
|
6 | 4 5 | eqeltrdi | |
7 | nnord | |
|
8 | ordunisuc | |
|
9 | 7 8 | syl | |
10 | id | |
|
11 | 9 10 | eqeltrd | |
12 | unieq | |
|
13 | 12 | eleq1d | |
14 | 11 13 | syl5ibrcom | |
15 | 14 | rexlimiv | |
16 | 6 15 | jaoi | |
17 | 1 16 | syl | |