Step |
Hyp |
Ref |
Expression |
1 |
|
caragendifcl.o |
|
2 |
|
caragendifcl.s |
|
3 |
|
caragendifcl.e |
|
4 |
|
eqid |
|
5 |
2
|
caragenss |
|
6 |
1 5
|
syl |
|
7 |
6
|
unissd |
|
8 |
7
|
ssdifssd |
|
9 |
2
|
fvexi |
|
10 |
9
|
uniex |
|
11 |
|
difexg |
|
12 |
10 11
|
ax-mp |
|
13 |
12
|
a1i |
|
14 |
|
elpwg |
|
15 |
13 14
|
syl |
|
16 |
8 15
|
mpbird |
|
17 |
|
elpwi |
|
18 |
17
|
adantl |
|
19 |
1 2
|
caragenuni |
|
20 |
19
|
eqcomd |
|
21 |
20
|
adantr |
|
22 |
18 21
|
sseqtrd |
|
23 |
|
difin2 |
|
24 |
22 23
|
syl |
|
25 |
|
incom |
|
26 |
25
|
a1i |
|
27 |
24 26
|
eqtr2d |
|
28 |
27
|
fveq2d |
|
29 |
22
|
ssdifd |
|
30 |
|
sscon |
|
31 |
29 30
|
syl |
|
32 |
|
dfin4 |
|
33 |
32
|
a1i |
|
34 |
|
eqimss2 |
|
35 |
33 34
|
syl |
|
36 |
31 35
|
sstrd |
|
37 |
|
elinel1 |
|
38 |
|
elinel2 |
|
39 |
|
elndif |
|
40 |
38 39
|
syl |
|
41 |
37 40
|
eldifd |
|
42 |
41
|
ssriv |
|
43 |
42
|
a1i |
|
44 |
36 43
|
eqssd |
|
45 |
44
|
fveq2d |
|
46 |
28 45
|
oveq12d |
|
47 |
|
iccssxr |
|
48 |
1
|
adantr |
|
49 |
18
|
ssdifssd |
|
50 |
48 4 49
|
omecl |
|
51 |
47 50
|
sseldi |
|
52 |
|
ssinss1 |
|
53 |
17 52
|
syl |
|
54 |
53
|
adantl |
|
55 |
48 4 54
|
omecl |
|
56 |
47 55
|
sseldi |
|
57 |
51 56
|
xaddcomd |
|
58 |
1 2
|
caragenel |
|
59 |
3 58
|
mpbid |
|
60 |
59
|
simprd |
|
61 |
60
|
r19.21bi |
|
62 |
46 57 61
|
3eqtrd |
|
63 |
1 4 2 16 62
|
carageneld |
|