Step |
Hyp |
Ref |
Expression |
1 |
|
metcn.2 |
|
2 |
|
metcn.4 |
|
3 |
1 2
|
metcnpi2 |
|
4 |
|
rphalfcl |
|
5 |
4
|
ad2antrl |
|
6 |
|
simplll |
|
7 |
|
simprr |
|
8 |
|
simplrl |
|
9 |
|
eqid |
|
10 |
9
|
cnprcl |
|
11 |
8 10
|
syl |
|
12 |
1
|
mopnuni |
|
13 |
6 12
|
syl |
|
14 |
11 13
|
eleqtrrd |
|
15 |
|
xmetcl |
|
16 |
6 7 14 15
|
syl3anc |
|
17 |
4
|
ad2antrl |
|
18 |
17
|
rpxrd |
|
19 |
|
rpxr |
|
20 |
19
|
ad2antrl |
|
21 |
|
rphalflt |
|
22 |
21
|
ad2antrl |
|
23 |
|
xrlelttr |
|
24 |
23
|
expcomd |
|
25 |
24
|
imp |
|
26 |
16 18 20 22 25
|
syl31anc |
|
27 |
|
simpllr |
|
28 |
1
|
mopntopon |
|
29 |
6 28
|
syl |
|
30 |
2
|
mopntopon |
|
31 |
27 30
|
syl |
|
32 |
|
cnpf2 |
|
33 |
29 31 8 32
|
syl3anc |
|
34 |
33 7
|
ffvelrnd |
|
35 |
33 14
|
ffvelrnd |
|
36 |
|
xmetcl |
|
37 |
27 34 35 36
|
syl3anc |
|
38 |
|
simplrr |
|
39 |
38
|
rpxrd |
|
40 |
|
xrltle |
|
41 |
37 39 40
|
syl2anc |
|
42 |
26 41
|
imim12d |
|
43 |
42
|
anassrs |
|
44 |
43
|
ralimdva |
|
45 |
44
|
impr |
|
46 |
|
breq2 |
|
47 |
46
|
rspceaimv |
|
48 |
5 45 47
|
syl2anc |
|
49 |
3 48
|
rexlimddv |
|