Description: If A is less than or equal to ordinal B , then the made set of A is included in the made set of B . (Contributed by Scott Fenton, 9-Oct-2024)
Ref | Expression | ||
---|---|---|---|
Assertion | madess | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imass2 | |
|
2 | 1 | unissd | |
3 | 2 | sspwd | |
4 | 3 | adantl | |
5 | 4 | adantl | |
6 | ssrexv | |
|
7 | 5 6 | syl | |
8 | ssrexv | |
|
9 | 5 8 | syl | |
10 | 9 | reximdv | |
11 | 7 10 | syld | |
12 | 11 | adantr | |
13 | 12 | ss2rabdv | |
14 | madeval2 | |
|
15 | 14 | adantr | |
16 | madeval2 | |
|
17 | 16 | adantr | |
18 | 17 | adantl | |
19 | 13 15 18 | 3sstr4d | |
20 | madef | |
|
21 | 20 | fdmi | |
22 | 21 | eleq2i | |
23 | ndmfv | |
|
24 | 22 23 | sylnbir | |
25 | 0ss | |
|
26 | 24 25 | eqsstrdi | |
27 | 26 | adantr | |
28 | 19 27 | pm2.61ian | |