Step |
Hyp |
Ref |
Expression |
1 |
|
cncmp.2 |
|
2 |
|
cntop2 |
|
3 |
2
|
3ad2ant3 |
|
4 |
|
elpwi |
|
5 |
|
simpl1 |
|
6 |
|
simpl3 |
|
7 |
|
simprl |
|
8 |
7
|
sselda |
|
9 |
|
cnima |
|
10 |
6 8 9
|
syl2an2r |
|
11 |
10
|
fmpttd |
|
12 |
11
|
frnd |
|
13 |
|
simprr |
|
14 |
13
|
imaeq2d |
|
15 |
|
eqid |
|
16 |
15 1
|
cnf |
|
17 |
6 16
|
syl |
|
18 |
|
fimacnv |
|
19 |
17 18
|
syl |
|
20 |
10
|
ralrimiva |
|
21 |
|
dfiun2g |
|
22 |
20 21
|
syl |
|
23 |
|
imauni |
|
24 |
|
eqid |
|
25 |
24
|
rnmpt |
|
26 |
25
|
unieqi |
|
27 |
22 23 26
|
3eqtr4g |
|
28 |
14 19 27
|
3eqtr3d |
|
29 |
15
|
cmpcov |
|
30 |
5 12 28 29
|
syl3anc |
|
31 |
|
elfpw |
|
32 |
|
simprll |
|
33 |
32
|
sselda |
|
34 |
|
simpll2 |
|
35 |
|
elssuni |
|
36 |
35 1
|
sseqtrrdi |
|
37 |
8 36
|
syl |
|
38 |
|
foimacnv |
|
39 |
34 37 38
|
syl2anc |
|
40 |
|
simpr |
|
41 |
39 40
|
eqeltrd |
|
42 |
41
|
ralrimiva |
|
43 |
|
imaeq2 |
|
44 |
43
|
eleq1d |
|
45 |
24 44
|
ralrnmptw |
|
46 |
20 45
|
syl |
|
47 |
42 46
|
mpbird |
|
48 |
47
|
adantr |
|
49 |
48
|
r19.21bi |
|
50 |
33 49
|
syldan |
|
51 |
50
|
fmpttd |
|
52 |
51
|
frnd |
|
53 |
|
simprlr |
|
54 |
|
eqid |
|
55 |
54
|
rnmpt |
|
56 |
|
abrexfi |
|
57 |
55 56
|
eqeltrid |
|
58 |
53 57
|
syl |
|
59 |
|
elfpw |
|
60 |
52 58 59
|
sylanbrc |
|
61 |
17
|
adantr |
|
62 |
61
|
fdmd |
|
63 |
|
simpll2 |
|
64 |
|
fof |
|
65 |
|
fdm |
|
66 |
63 64 65
|
3syl |
|
67 |
|
simprr |
|
68 |
62 66 67
|
3eqtr3d |
|
69 |
68
|
imaeq2d |
|
70 |
|
foima |
|
71 |
63 70
|
syl |
|
72 |
50
|
ralrimiva |
|
73 |
|
dfiun2g |
|
74 |
72 73
|
syl |
|
75 |
|
imauni |
|
76 |
55
|
unieqi |
|
77 |
74 75 76
|
3eqtr4g |
|
78 |
69 71 77
|
3eqtr3d |
|
79 |
|
unieq |
|
80 |
79
|
rspceeqv |
|
81 |
60 78 80
|
syl2anc |
|
82 |
81
|
expr |
|
83 |
31 82
|
sylan2b |
|
84 |
83
|
rexlimdva |
|
85 |
30 84
|
mpd |
|
86 |
85
|
expr |
|
87 |
4 86
|
sylan2 |
|
88 |
87
|
ralrimiva |
|
89 |
1
|
iscmp |
|
90 |
3 88 89
|
sylanbrc |
|