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