Description: Lemma for noeta . The restriction of W to the domain of T is T . (Contributed by Scott Fenton, 9-Aug-2024)
Ref | Expression | ||
---|---|---|---|
Hypotheses | noetainflem.1 | |
|
noetainflem.2 | |
||
Assertion | noetainflem2 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noetainflem.1 | |
|
2 | noetainflem.2 | |
|
3 | 2 | reseq1i | |
4 | resundir | |
|
5 | 3 4 | eqtri | |
6 | 1 | noinfno | |
7 | nofun | |
|
8 | 6 7 | syl | |
9 | funrel | |
|
10 | resdm | |
|
11 | 8 9 10 | 3syl | |
12 | dmres | |
|
13 | 2oex | |
|
14 | 13 | snnz | |
15 | dmxp | |
|
16 | 14 15 | ax-mp | |
17 | 16 | ineq2i | |
18 | disjdif | |
|
19 | 17 18 | eqtri | |
20 | 12 19 | eqtri | |
21 | relres | |
|
22 | reldm0 | |
|
23 | 21 22 | ax-mp | |
24 | 20 23 | mpbir | |
25 | 24 | a1i | |
26 | 11 25 | uneq12d | |
27 | un0 | |
|
28 | 26 27 | eqtrdi | |
29 | 5 28 | eqtrid | |