Step |
Hyp |
Ref |
Expression |
1 |
|
domunsncan.a |
|
2 |
|
domunsncan.b |
|
3 |
|
ssun2 |
|
4 |
|
reldom |
|
5 |
4
|
brrelex2i |
|
6 |
5
|
adantl |
|
7 |
|
ssexg |
|
8 |
3 6 7
|
sylancr |
|
9 |
|
brdomi |
|
10 |
|
vex |
|
11 |
10
|
resex |
|
12 |
|
simprr |
|
13 |
|
difss |
|
14 |
|
f1ores |
|
15 |
12 13 14
|
sylancl |
|
16 |
|
f1oen3g |
|
17 |
11 15 16
|
sylancr |
|
18 |
|
df-f1 |
|
19 |
|
imadif |
|
20 |
18 19
|
simplbiim |
|
21 |
20
|
ad2antll |
|
22 |
|
snex |
|
23 |
|
simprl |
|
24 |
|
unexg |
|
25 |
22 23 24
|
sylancr |
|
26 |
|
difexg |
|
27 |
25 26
|
syl |
|
28 |
|
f1f |
|
29 |
|
fimass |
|
30 |
28 29
|
syl |
|
31 |
30
|
ad2antll |
|
32 |
31
|
ssdifd |
|
33 |
|
f1fn |
|
34 |
33
|
ad2antll |
|
35 |
1
|
snid |
|
36 |
|
elun1 |
|
37 |
35 36
|
ax-mp |
|
38 |
|
fnsnfv |
|
39 |
34 37 38
|
sylancl |
|
40 |
39
|
difeq2d |
|
41 |
32 40
|
sseqtrrd |
|
42 |
|
ssdomg |
|
43 |
27 41 42
|
sylc |
|
44 |
|
ffvelrn |
|
45 |
28 37 44
|
sylancl |
|
46 |
45
|
ad2antll |
|
47 |
2
|
snid |
|
48 |
|
elun1 |
|
49 |
47 48
|
mp1i |
|
50 |
|
difsnen |
|
51 |
25 46 49 50
|
syl3anc |
|
52 |
|
domentr |
|
53 |
43 51 52
|
syl2anc |
|
54 |
21 53
|
eqbrtrd |
|
55 |
|
endomtr |
|
56 |
17 54 55
|
syl2anc |
|
57 |
|
uncom |
|
58 |
57
|
difeq1i |
|
59 |
|
difun2 |
|
60 |
58 59
|
eqtri |
|
61 |
|
difsn |
|
62 |
60 61
|
syl5eq |
|
63 |
62
|
ad2antrr |
|
64 |
|
uncom |
|
65 |
64
|
difeq1i |
|
66 |
|
difun2 |
|
67 |
65 66
|
eqtri |
|
68 |
|
difsn |
|
69 |
67 68
|
syl5eq |
|
70 |
69
|
ad2antlr |
|
71 |
56 63 70
|
3brtr3d |
|
72 |
71
|
expr |
|
73 |
72
|
exlimdv |
|
74 |
9 73
|
syl5 |
|
75 |
74
|
impancom |
|
76 |
8 75
|
mpd |
|
77 |
|
en2sn |
|
78 |
1 2 77
|
mp2an |
|
79 |
|
endom |
|
80 |
78 79
|
mp1i |
|
81 |
|
simpr |
|
82 |
|
incom |
|
83 |
|
disjsn |
|
84 |
83
|
biimpri |
|
85 |
82 84
|
syl5eq |
|
86 |
85
|
ad2antlr |
|
87 |
|
undom |
|
88 |
80 81 86 87
|
syl21anc |
|
89 |
76 88
|
impbida |
|