Step |
Hyp |
Ref |
Expression |
1 |
|
simpr |
|
2 |
1
|
oveq1d |
|
3 |
|
simplr |
|
4 |
|
idd |
|
5 |
4 1
|
jctird |
|
6 |
3 5
|
mtod |
|
7 |
6
|
neqned |
|
8 |
|
map0b |
|
9 |
7 8
|
syl |
|
10 |
2 9
|
eqtrd |
|
11 |
|
ovex |
|
12 |
11
|
0dom |
|
13 |
10 12
|
eqbrtrdi |
|
14 |
|
simpll |
|
15 |
|
reldom |
|
16 |
15
|
brrelex2i |
|
17 |
16
|
ad2antrr |
|
18 |
|
domeng |
|
19 |
17 18
|
syl |
|
20 |
14 19
|
mpbid |
|
21 |
|
enrefg |
|
22 |
21
|
ad2antlr |
|
23 |
|
simprrl |
|
24 |
|
mapen |
|
25 |
22 23 24
|
syl2anc |
|
26 |
|
ovexd |
|
27 |
|
ovexd |
|
28 |
|
simprl |
|
29 |
|
simplr |
|
30 |
16
|
ad2antrr |
|
31 |
|
difexg |
|
32 |
30 31
|
syl |
|
33 |
|
map0g |
|
34 |
|
simpl |
|
35 |
33 34
|
syl6bi |
|
36 |
35
|
necon3d |
|
37 |
29 32 36
|
syl2anc |
|
38 |
28 37
|
mpd |
|
39 |
|
xpdom3 |
|
40 |
26 27 38 39
|
syl3anc |
|
41 |
|
vex |
|
42 |
41
|
a1i |
|
43 |
|
disjdif |
|
44 |
43
|
a1i |
|
45 |
|
mapunen |
|
46 |
42 32 29 44 45
|
syl31anc |
|
47 |
46
|
ensymd |
|
48 |
|
simprrr |
|
49 |
|
undif |
|
50 |
48 49
|
sylib |
|
51 |
50
|
oveq2d |
|
52 |
47 51
|
breqtrd |
|
53 |
|
domentr |
|
54 |
40 52 53
|
syl2anc |
|
55 |
|
endomtr |
|
56 |
25 54 55
|
syl2anc |
|
57 |
56
|
expr |
|
58 |
57
|
exlimdv |
|
59 |
20 58
|
mpd |
|
60 |
59
|
adantlr |
|
61 |
13 60
|
pm2.61dane |
|
62 |
61
|
an32s |
|
63 |
62
|
ex |
|
64 |
|
reldmmap |
|
65 |
64
|
ovprc1 |
|
66 |
65 12
|
eqbrtrdi |
|
67 |
63 66
|
pm2.61d1 |
|