Step |
Hyp |
Ref |
Expression |
1 |
|
lecldbas.1 |
|
2 |
|
eqid |
|
3 |
|
eqid |
|
4 |
2 3
|
leordtval2 |
|
5 |
|
fvex |
|
6 |
|
fvex |
|
7 |
|
iccf |
|
8 |
|
ffn |
|
9 |
7 8
|
ax-mp |
|
10 |
|
ovelrn |
|
11 |
9 10
|
ax-mp |
|
12 |
|
difeq2 |
|
13 |
|
iccordt |
|
14 |
|
letopuni |
|
15 |
14
|
cldopn |
|
16 |
13 15
|
ax-mp |
|
17 |
12 16
|
eqeltrdi |
|
18 |
17
|
rexlimivw |
|
19 |
18
|
rexlimivw |
|
20 |
11 19
|
sylbi |
|
21 |
1 20
|
fmpti |
|
22 |
|
frn |
|
23 |
21 22
|
ax-mp |
|
24 |
6 23
|
ssexi |
|
25 |
|
eqid |
|
26 |
|
mnfxr |
|
27 |
|
fnovrn |
|
28 |
9 26 27
|
mp3an12 |
|
29 |
26
|
a1i |
|
30 |
|
id |
|
31 |
|
pnfxr |
|
32 |
31
|
a1i |
|
33 |
|
mnfle |
|
34 |
|
pnfge |
|
35 |
|
df-icc |
|
36 |
|
df-ioc |
|
37 |
|
xrltnle |
|
38 |
|
xrletr |
|
39 |
|
xrlelttr |
|
40 |
|
xrltle |
|
41 |
40
|
3adant2 |
|
42 |
39 41
|
syld |
|
43 |
35 36 37 35 38 42
|
ixxun |
|
44 |
29 30 32 33 34 43
|
syl32anc |
|
45 |
|
iccmax |
|
46 |
44 45
|
eqtrdi |
|
47 |
|
iccssxr |
|
48 |
35 36 37
|
ixxdisj |
|
49 |
26 31 48
|
mp3an13 |
|
50 |
|
uneqdifeq |
|
51 |
47 49 50
|
sylancr |
|
52 |
46 51
|
mpbid |
|
53 |
52
|
eqcomd |
|
54 |
|
difeq2 |
|
55 |
54
|
rspceeqv |
|
56 |
28 53 55
|
syl2anc |
|
57 |
|
xrex |
|
58 |
57
|
difexi |
|
59 |
1 58
|
elrnmpti |
|
60 |
56 59
|
sylibr |
|
61 |
25 60
|
fmpti |
|
62 |
|
frn |
|
63 |
61 62
|
ax-mp |
|
64 |
|
eqid |
|
65 |
|
fnovrn |
|
66 |
9 31 65
|
mp3an13 |
|
67 |
|
df-ico |
|
68 |
|
xrlenlt |
|
69 |
|
xrltletr |
|
70 |
|
xrltle |
|
71 |
70
|
3adant2 |
|
72 |
69 71
|
syld |
|
73 |
|
xrletr |
|
74 |
67 35 68 35 72 73
|
ixxun |
|
75 |
29 30 32 33 34 74
|
syl32anc |
|
76 |
|
uncom |
|
77 |
75 76 45
|
3eqtr3g |
|
78 |
|
iccssxr |
|
79 |
|
incom |
|
80 |
67 35 68
|
ixxdisj |
|
81 |
26 31 80
|
mp3an13 |
|
82 |
79 81
|
eqtrid |
|
83 |
|
uneqdifeq |
|
84 |
78 82 83
|
sylancr |
|
85 |
77 84
|
mpbid |
|
86 |
85
|
eqcomd |
|
87 |
|
difeq2 |
|
88 |
87
|
rspceeqv |
|
89 |
66 86 88
|
syl2anc |
|
90 |
1 58
|
elrnmpti |
|
91 |
89 90
|
sylibr |
|
92 |
64 91
|
fmpti |
|
93 |
|
frn |
|
94 |
92 93
|
ax-mp |
|
95 |
63 94
|
unssi |
|
96 |
|
fiss |
|
97 |
24 95 96
|
mp2an |
|
98 |
|
tgss |
|
99 |
5 97 98
|
mp2an |
|
100 |
4 99
|
eqsstri |
|
101 |
|
letop |
|
102 |
|
tgfiss |
|
103 |
101 23 102
|
mp2an |
|
104 |
100 103
|
eqssi |
|