Description: The predicate W is a uniform space. (Contributed by Thierry Arnoux, 4-Dec-2017)
Ref | Expression | ||
---|---|---|---|
Hypotheses | isusp.1 | |
|
isusp.2 | |
||
isusp.3 | |
||
Assertion | isusp | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isusp.1 | |
|
2 | isusp.2 | |
|
3 | isusp.3 | |
|
4 | elex | |
|
5 | 0nep0 | |
|
6 | fvprc | |
|
7 | 1 6 | eqtrid | |
8 | 7 | fveq2d | |
9 | ust0 | |
|
10 | 8 9 | eqtrdi | |
11 | 10 | eleq2d | |
12 | 2 | fvexi | |
13 | 12 | elsn | |
14 | 11 13 | bitrdi | |
15 | fvprc | |
|
16 | 2 15 | eqtrid | |
17 | 16 | eqeq1d | |
18 | 14 17 | bitrd | |
19 | 18 | necon3bbid | |
20 | 5 19 | mpbiri | |
21 | 20 | con4i | |
22 | 21 | adantr | |
23 | fveq2 | |
|
24 | 23 2 | eqtr4di | |
25 | fveq2 | |
|
26 | 25 1 | eqtr4di | |
27 | 26 | fveq2d | |
28 | 24 27 | eleq12d | |
29 | fveq2 | |
|
30 | 29 3 | eqtr4di | |
31 | 24 | fveq2d | |
32 | 30 31 | eqeq12d | |
33 | 28 32 | anbi12d | |
34 | df-usp | |
|
35 | 33 34 | elab2g | |
36 | 4 22 35 | pm5.21nii | |