Step |
Hyp |
Ref |
Expression |
1 |
|
ima0 |
|
2 |
|
imaeq2 |
|
3 |
|
imaeq2 |
|
4 |
|
ima0 |
|
5 |
3 4
|
eqtrdi |
|
6 |
5
|
difeq1d |
|
7 |
|
0dif |
|
8 |
6 7
|
eqtrdi |
|
9 |
1 2 8
|
3eqtr4a |
|
10 |
9
|
adantl |
|
11 |
|
uncom |
|
12 |
|
un0 |
|
13 |
11 12
|
eqtr2i |
|
14 |
|
inundif |
|
15 |
14
|
imaeq1i |
|
16 |
|
imaundir |
|
17 |
15 16
|
eqtr3i |
|
18 |
17
|
difeq1i |
|
19 |
|
difundir |
|
20 |
18 19
|
eqtri |
|
21 |
|
inss2 |
|
22 |
|
imass1 |
|
23 |
|
ssdif |
|
24 |
21 22 23
|
mp2b |
|
25 |
|
xpima |
|
26 |
|
incom |
|
27 |
|
df-ss |
|
28 |
27
|
biimpi |
|
29 |
26 28
|
syl5eqr |
|
30 |
29
|
adantl |
|
31 |
|
simpl |
|
32 |
30 31
|
eqnetrd |
|
33 |
|
neneq |
|
34 |
|
iffalse |
|
35 |
32 33 34
|
3syl |
|
36 |
25 35
|
syl5eq |
|
37 |
36
|
difeq1d |
|
38 |
|
difid |
|
39 |
37 38
|
eqtrdi |
|
40 |
24 39
|
sseqtrid |
|
41 |
|
ss0 |
|
42 |
40 41
|
syl |
|
43 |
|
df-ima |
|
44 |
|
df-res |
|
45 |
44
|
rneqi |
|
46 |
43 45
|
eqtri |
|
47 |
46
|
ineq1i |
|
48 |
|
xpss1 |
|
49 |
|
sslin |
|
50 |
|
rnss |
|
51 |
48 49 50
|
3syl |
|
52 |
|
ssn0 |
|
53 |
52
|
ancoms |
|
54 |
|
inss1 |
|
55 |
|
ssdif |
|
56 |
54 55
|
ax-mp |
|
57 |
|
incom |
|
58 |
|
indif2 |
|
59 |
57 58
|
eqtr3i |
|
60 |
|
difxp2 |
|
61 |
56 59 60
|
3sstr4i |
|
62 |
|
rnss |
|
63 |
61 62
|
mp1i |
|
64 |
|
rnxp |
|
65 |
63 64
|
sseqtrd |
|
66 |
|
disj2 |
|
67 |
65 66
|
sylibr |
|
68 |
53 67
|
syl |
|
69 |
|
ssdisj |
|
70 |
51 68 69
|
syl2an2 |
|
71 |
47 70
|
syl5eq |
|
72 |
|
disj3 |
|
73 |
71 72
|
sylib |
|
74 |
73
|
eqcomd |
|
75 |
42 74
|
uneq12d |
|
76 |
20 75
|
syl5eq |
|
77 |
13 76
|
eqtr4id |
|
78 |
77
|
ancoms |
|
79 |
10 78
|
pm2.61dane |
|