Step |
Hyp |
Ref |
Expression |
1 |
|
difeq2 |
|
2 |
1
|
breq1d |
|
3 |
2
|
elrab |
|
4 |
|
velpw |
|
5 |
4
|
anbi1i |
|
6 |
3 5
|
bitri |
|
7 |
6
|
a1i |
|
8 |
|
simpl |
|
9 |
|
difid |
|
10 |
|
infn0 |
|
11 |
10
|
adantl |
|
12 |
|
0sdomg |
|
13 |
12
|
adantr |
|
14 |
11 13
|
mpbird |
|
15 |
9 14
|
eqbrtrid |
|
16 |
|
difeq2 |
|
17 |
16
|
breq1d |
|
18 |
17
|
sbcieg |
|
19 |
18
|
adantr |
|
20 |
15 19
|
mpbird |
|
21 |
|
sdomirr |
|
22 |
|
0ex |
|
23 |
|
difeq2 |
|
24 |
|
dif0 |
|
25 |
23 24
|
eqtrdi |
|
26 |
25
|
breq1d |
|
27 |
22 26
|
sbcie |
|
28 |
27
|
a1i |
|
29 |
21 28
|
mtbiri |
|
30 |
|
simp1l |
|
31 |
|
difexg |
|
32 |
30 31
|
syl |
|
33 |
|
sscon |
|
34 |
33
|
3ad2ant3 |
|
35 |
|
ssdomg |
|
36 |
32 34 35
|
sylc |
|
37 |
|
domsdomtr |
|
38 |
37
|
ex |
|
39 |
36 38
|
syl |
|
40 |
|
vex |
|
41 |
|
difeq2 |
|
42 |
41
|
breq1d |
|
43 |
40 42
|
sbcie |
|
44 |
|
vex |
|
45 |
|
difeq2 |
|
46 |
45
|
breq1d |
|
47 |
44 46
|
sbcie |
|
48 |
39 43 47
|
3imtr4g |
|
49 |
|
infunsdom |
|
50 |
49
|
ex |
|
51 |
|
difindi |
|
52 |
51
|
breq1i |
|
53 |
50 52
|
syl6ibr |
|
54 |
53
|
3ad2ant1 |
|
55 |
47 43
|
anbi12i |
|
56 |
44
|
inex1 |
|
57 |
|
difeq2 |
|
58 |
57
|
breq1d |
|
59 |
56 58
|
sbcie |
|
60 |
54 55 59
|
3imtr4g |
|
61 |
7 8 20 29 48 60
|
isfild |
|