Step |
Hyp |
Ref |
Expression |
1 |
|
iundisj2fi.0 |
|
2 |
|
iundisj2fi.1 |
|
3 |
|
tru |
|
4 |
|
eqeq12 |
|
5 |
|
csbeq1 |
|
6 |
|
csbeq1 |
|
7 |
5 6
|
ineqan12d |
|
8 |
7
|
eqeq1d |
|
9 |
4 8
|
orbi12d |
|
10 |
|
eqeq12 |
|
11 |
|
equcom |
|
12 |
10 11
|
syl6bb |
|
13 |
|
csbeq1 |
|
14 |
|
csbeq1 |
|
15 |
13 14
|
ineqan12d |
|
16 |
|
incom |
|
17 |
15 16
|
eqtrdi |
|
18 |
17
|
eqeq1d |
|
19 |
12 18
|
orbi12d |
|
20 |
|
fzossnn |
|
21 |
|
nnssre |
|
22 |
20 21
|
sstri |
|
23 |
22
|
a1i |
|
24 |
|
biidd |
|
25 |
|
nesym |
|
26 |
22
|
sseli |
|
27 |
22
|
sseli |
|
28 |
|
id |
|
29 |
|
leltne |
|
30 |
26 27 28 29
|
syl3an |
|
31 |
|
vex |
|
32 |
|
nfcsb1v |
|
33 |
|
nfcv |
|
34 |
33 1
|
nfiun |
|
35 |
32 34
|
nfdif |
|
36 |
|
csbeq1a |
|
37 |
|
oveq2 |
|
38 |
37
|
iuneq1d |
|
39 |
36 38
|
difeq12d |
|
40 |
31 35 39
|
csbief |
|
41 |
|
vex |
|
42 |
|
nfcsb1v |
|
43 |
|
nfcv |
|
44 |
43 1
|
nfiun |
|
45 |
42 44
|
nfdif |
|
46 |
|
csbeq1a |
|
47 |
|
oveq2 |
|
48 |
47
|
iuneq1d |
|
49 |
46 48
|
difeq12d |
|
50 |
41 45 49
|
csbief |
|
51 |
40 50
|
ineq12i |
|
52 |
|
simp1 |
|
53 |
20 52
|
sseldi |
|
54 |
|
nnuz |
|
55 |
53 54
|
eleqtrdi |
|
56 |
|
simp2 |
|
57 |
20 56
|
sseldi |
|
58 |
57
|
nnzd |
|
59 |
|
simp3 |
|
60 |
|
elfzo2 |
|
61 |
55 58 59 60
|
syl3anbrc |
|
62 |
|
nfcv |
|
63 |
62 1 2
|
csbhypf |
|
64 |
63
|
equcoms |
|
65 |
64
|
eqcomd |
|
66 |
65
|
ssiun2s |
|
67 |
61 66
|
syl |
|
68 |
67
|
ssdifssd |
|
69 |
68
|
ssrind |
|
70 |
51 69
|
eqsstrid |
|
71 |
|
disjdif |
|
72 |
|
sseq0 |
|
73 |
70 71 72
|
sylancl |
|
74 |
73
|
3expia |
|
75 |
74
|
3adant3 |
|
76 |
30 75
|
sylbird |
|
77 |
25 76
|
syl5bir |
|
78 |
77
|
orrd |
|
79 |
78
|
adantl |
|
80 |
9 19 23 24 79
|
wlogle |
|
81 |
3 80
|
mpan |
|
82 |
81
|
rgen2 |
|
83 |
|
disjors |
|
84 |
82 83
|
mpbir |
|