Step |
Hyp |
Ref |
Expression |
1 |
|
xrsxmet.1 |
|
2 |
|
xrsmopn.1 |
|
3 |
|
elssuni |
|
4 |
|
letopuni |
|
5 |
3 4
|
sseqtrrdi |
|
6 |
|
eqid |
|
7 |
6
|
rexmet |
|
8 |
|
letop |
|
9 |
|
reex |
|
10 |
|
elrestr |
|
11 |
8 9 10
|
mp3an12 |
|
12 |
11
|
ad2antrr |
|
13 |
|
elin |
|
14 |
13
|
biimpri |
|
15 |
14
|
adantll |
|
16 |
|
eqid |
|
17 |
16
|
xrtgioo |
|
18 |
|
eqid |
|
19 |
6 18
|
tgioo |
|
20 |
17 19
|
eqtr3i |
|
21 |
20
|
mopni2 |
|
22 |
7 12 15 21
|
mp3an2i |
|
23 |
1
|
xrsxmet |
|
24 |
|
simplr |
|
25 |
|
ressxr |
|
26 |
|
sseqin2 |
|
27 |
25 26
|
mpbi |
|
28 |
24 27
|
eleqtrrdi |
|
29 |
|
rpxr |
|
30 |
29
|
adantl |
|
31 |
1
|
xrsdsre |
|
32 |
31
|
eqcomi |
|
33 |
32
|
blres |
|
34 |
23 28 30 33
|
mp3an2i |
|
35 |
1
|
xrsblre |
|
36 |
29 35
|
sylan2 |
|
37 |
36
|
adantll |
|
38 |
|
df-ss |
|
39 |
37 38
|
sylib |
|
40 |
34 39
|
eqtrd |
|
41 |
40
|
sseq1d |
|
42 |
|
inss1 |
|
43 |
|
sstr |
|
44 |
42 43
|
mpan2 |
|
45 |
41 44
|
syl6bi |
|
46 |
45
|
reximdva |
|
47 |
22 46
|
mpd |
|
48 |
|
1rp |
|
49 |
5
|
sselda |
|
50 |
49
|
adantr |
|
51 |
|
rpxr |
|
52 |
48 51
|
mp1i |
|
53 |
|
elbl |
|
54 |
23 50 52 53
|
mp3an2i |
|
55 |
|
simp2 |
|
56 |
49
|
3ad2ant1 |
|
57 |
56
|
adantr |
|
58 |
|
simpl3l |
|
59 |
|
xmetcl |
|
60 |
23 57 58 59
|
mp3an2i |
|
61 |
|
1red |
|
62 |
|
xmetge0 |
|
63 |
23 57 58 62
|
mp3an2i |
|
64 |
|
simpl3r |
|
65 |
|
1xr |
|
66 |
|
xrltle |
|
67 |
60 65 66
|
sylancl |
|
68 |
64 67
|
mpd |
|
69 |
|
xrrege0 |
|
70 |
60 61 63 68 69
|
syl22anc |
|
71 |
|
simpr |
|
72 |
1
|
xrsdsreclb |
|
73 |
57 58 71 72
|
syl3anc |
|
74 |
70 73
|
mpbid |
|
75 |
74
|
simpld |
|
76 |
75
|
ex |
|
77 |
76
|
necon1bd |
|
78 |
|
simp1r |
|
79 |
|
elequ1 |
|
80 |
78 79
|
syl5ibcom |
|
81 |
77 80
|
syld |
|
82 |
55 81
|
mpd |
|
83 |
82
|
3expia |
|
84 |
54 83
|
sylbid |
|
85 |
84
|
ssrdv |
|
86 |
|
oveq2 |
|
87 |
86
|
sseq1d |
|
88 |
87
|
rspcev |
|
89 |
48 85 88
|
sylancr |
|
90 |
47 89
|
pm2.61dan |
|
91 |
90
|
ralrimiva |
|
92 |
2
|
elmopn2 |
|
93 |
23 92
|
ax-mp |
|
94 |
5 91 93
|
sylanbrc |
|
95 |
94
|
ssriv |
|