Step |
Hyp |
Ref |
Expression |
1 |
|
coiun |
|
2 |
|
inss1 |
|
3 |
|
fndm |
|
4 |
2 3
|
sseqtrid |
|
5 |
|
dfco2a |
|
6 |
4 5
|
syl |
|
7 |
6
|
coeq2d |
|
8 |
|
inss1 |
|
9 |
|
dmxpss |
|
10 |
8 9
|
sstri |
|
11 |
|
dfco2a |
|
12 |
10 11
|
ax-mp |
|
13 |
|
fvex |
|
14 |
|
fparlem2 |
|
15 |
|
sneq |
|
16 |
15
|
xpeq2d |
|
17 |
14 16
|
syl5eq |
|
18 |
15
|
imaeq2d |
|
19 |
|
df-ima |
|
20 |
|
ssid |
|
21 |
|
xpssres |
|
22 |
20 21
|
ax-mp |
|
23 |
22
|
rneqi |
|
24 |
13
|
snnz |
|
25 |
|
rnxp |
|
26 |
24 25
|
ax-mp |
|
27 |
23 26
|
eqtri |
|
28 |
19 27
|
eqtri |
|
29 |
18 28
|
eqtrdi |
|
30 |
17 29
|
xpeq12d |
|
31 |
13 30
|
iunxsn |
|
32 |
12 31
|
eqtri |
|
33 |
32
|
cnveqi |
|
34 |
|
cnvco |
|
35 |
|
cnvxp |
|
36 |
33 34 35
|
3eqtr3i |
|
37 |
|
fparlem2 |
|
38 |
37
|
xpeq2i |
|
39 |
|
fnsnfv |
|
40 |
39
|
xpeq1d |
|
41 |
38 40
|
syl5eqr |
|
42 |
41
|
cnveqd |
|
43 |
|
cnvxp |
|
44 |
42 43
|
eqtrdi |
|
45 |
44
|
coeq2d |
|
46 |
36 45
|
syl5eqr |
|
47 |
46
|
iuneq2dv |
|
48 |
1 7 47
|
3eqtr4a |
|