Step |
Hyp |
Ref |
Expression |
1 |
|
hauseqcn.x |
|
2 |
|
hauseqcn.k |
|
3 |
|
hauseqcn.f |
|
4 |
|
hauseqcn.g |
|
5 |
|
hauseqcn.e |
|
6 |
|
hauseqcn.a |
|
7 |
|
hauseqcn.c |
|
8 |
|
cntop1 |
|
9 |
3 8
|
syl |
|
10 |
|
dmin |
|
11 |
|
eqid |
|
12 |
|
eqid |
|
13 |
11 12
|
cnf |
|
14 |
|
fdm |
|
15 |
3 13 14
|
3syl |
|
16 |
11 12
|
cnf |
|
17 |
|
fdm |
|
18 |
4 16 17
|
3syl |
|
19 |
15 18
|
ineq12d |
|
20 |
|
inidm |
|
21 |
19 20
|
eqtrdi |
|
22 |
10 21
|
sseqtrid |
|
23 |
|
ffn |
|
24 |
3 13 23
|
3syl |
|
25 |
|
ffn |
|
26 |
4 16 25
|
3syl |
|
27 |
6 1
|
sseqtrdi |
|
28 |
|
fnreseql |
|
29 |
24 26 27 28
|
syl3anc |
|
30 |
5 29
|
mpbid |
|
31 |
11
|
clsss |
|
32 |
9 22 30 31
|
syl3anc |
|
33 |
2 3 4
|
hauseqlcld |
|
34 |
|
cldcls |
|
35 |
33 34
|
syl |
|
36 |
32 7 35
|
3sstr3d |
|
37 |
1 36
|
eqsstrrid |
|
38 |
|
fneqeql2 |
|
39 |
24 26 38
|
syl2anc |
|
40 |
37 39
|
mpbird |
|