Step |
Hyp |
Ref |
Expression |
1 |
|
elcls3.1 |
|
2 |
|
elcls3.2 |
|
3 |
|
elcls3.3 |
|
4 |
|
elcls3.4 |
|
5 |
|
elcls3.5 |
|
6 |
|
tgcl |
|
7 |
3 6
|
syl |
|
8 |
1 7
|
eqeltrd |
|
9 |
4 2
|
sseqtrd |
|
10 |
5 2
|
eleqtrd |
|
11 |
|
eqid |
|
12 |
11
|
elcls |
|
13 |
8 9 10 12
|
syl3anc |
|
14 |
|
bastg |
|
15 |
3 14
|
syl |
|
16 |
15 1
|
sseqtrrd |
|
17 |
16
|
sseld |
|
18 |
17
|
imim1d |
|
19 |
18
|
ralimdv2 |
|
20 |
|
eleq2w |
|
21 |
|
ineq1 |
|
22 |
21
|
neeq1d |
|
23 |
20 22
|
imbi12d |
|
24 |
23
|
cbvralvw |
|
25 |
19 24
|
syl6ib |
|
26 |
|
simprl |
|
27 |
1
|
ad2antrr |
|
28 |
26 27
|
eleqtrd |
|
29 |
|
simprr |
|
30 |
|
tg2 |
|
31 |
28 29 30
|
syl2anc |
|
32 |
|
eleq2w |
|
33 |
|
ineq1 |
|
34 |
33
|
neeq1d |
|
35 |
32 34
|
imbi12d |
|
36 |
35
|
rspccva |
|
37 |
36
|
imp |
|
38 |
|
ssdisj |
|
39 |
38
|
ex |
|
40 |
39
|
necon3d |
|
41 |
37 40
|
syl5com |
|
42 |
41
|
exp31 |
|
43 |
42
|
imp4a |
|
44 |
43
|
rexlimdv |
|
45 |
44
|
ad2antlr |
|
46 |
31 45
|
mpd |
|
47 |
46
|
exp43 |
|
48 |
47
|
ralrimdv |
|
49 |
25 48
|
impbid |
|
50 |
13 49
|
bitrd |
|