Step |
Hyp |
Ref |
Expression |
1 |
|
carageniuncl.o |
|
2 |
|
carageniuncl.s |
|
3 |
|
carageniuncl.3 |
|
4 |
|
carageniuncl.z |
|
5 |
|
carageniuncl.e |
|
6 |
|
eqid |
|
7 |
5
|
ffvelrnda |
|
8 |
|
elssuni |
|
9 |
7 8
|
syl |
|
10 |
1 2
|
caragenuni |
|
11 |
10
|
adantr |
|
12 |
9 11
|
sseqtrd |
|
13 |
12
|
ralrimiva |
|
14 |
|
iunss |
|
15 |
13 14
|
sylibr |
|
16 |
4
|
fvexi |
|
17 |
|
fvex |
|
18 |
16 17
|
iunex |
|
19 |
18
|
a1i |
|
20 |
|
elpwg |
|
21 |
19 20
|
syl |
|
22 |
15 21
|
mpbird |
|
23 |
|
iccssxr |
|
24 |
1
|
adantr |
|
25 |
|
elpwi |
|
26 |
|
ssinss1 |
|
27 |
25 26
|
syl |
|
28 |
27
|
adantl |
|
29 |
24 6 28
|
omecl |
|
30 |
23 29
|
sseldi |
|
31 |
25
|
adantl |
|
32 |
31
|
ssdifssd |
|
33 |
24 6 32
|
omecl |
|
34 |
23 33
|
sseldi |
|
35 |
30 34
|
xaddcld |
|
36 |
24 6 31
|
omecl |
|
37 |
23 36
|
sseldi |
|
38 |
|
pnfge |
|
39 |
35 38
|
syl |
|
40 |
39
|
adantr |
|
41 |
|
id |
|
42 |
41
|
eqcomd |
|
43 |
42
|
adantl |
|
44 |
40 43
|
breqtrd |
|
45 |
|
simpl |
|
46 |
|
rge0ssre |
|
47 |
|
0xr |
|
48 |
47
|
a1i |
|
49 |
|
pnfxr |
|
50 |
49
|
a1i |
|
51 |
45 36
|
syl |
|
52 |
41
|
necon3bi |
|
53 |
52
|
adantl |
|
54 |
48 50 51 53
|
eliccelicod |
|
55 |
46 54
|
sseldi |
|
56 |
24
|
ad2antrr |
|
57 |
31
|
ad2antrr |
|
58 |
|
simpr |
|
59 |
58
|
adantr |
|
60 |
3
|
ad3antrrr |
|
61 |
5
|
ad3antrrr |
|
62 |
|
simpr |
|
63 |
|
eqid |
|
64 |
|
fveq2 |
|
65 |
|
oveq2 |
|
66 |
65
|
iuneq1d |
|
67 |
64 66
|
difeq12d |
|
68 |
67
|
cbvmptv |
|
69 |
56 2 6 57 59 60 4 61 62 63 68
|
carageniuncllem2 |
|
70 |
69
|
ralrimiva |
|
71 |
35
|
adantr |
|
72 |
|
xralrple |
|
73 |
71 58 72
|
syl2anc |
|
74 |
70 73
|
mpbird |
|
75 |
45 55 74
|
syl2anc |
|
76 |
44 75
|
pm2.61dan |
|
77 |
24 6 31
|
omelesplit |
|
78 |
35 37 76 77
|
xrletrid |
|
79 |
1 6 2 22 78
|
carageneld |
|