Step |
Hyp |
Ref |
Expression |
1 |
|
simpl1 |
|
2 |
|
simpl2 |
|
3 |
|
simpr |
|
4 |
|
r19.26 |
|
5 |
2 3 4
|
sylanbrc |
|
6 |
|
simpl3 |
|
7 |
|
volfiniun |
|
8 |
1 5 6 7
|
syl3anc |
|
9 |
|
nfcv |
|
10 |
9
|
nfel1 |
|
11 |
|
nfra1 |
|
12 |
|
nfdisj1 |
|
13 |
10 11 12
|
nf3an |
|
14 |
|
nfra1 |
|
15 |
13 14
|
nfan |
|
16 |
3
|
r19.21bi |
|
17 |
|
rspa |
|
18 |
|
volf |
|
19 |
18
|
ffvelrni |
|
20 |
17 19
|
syl |
|
21 |
2 20
|
sylan |
|
22 |
|
0xr |
|
23 |
|
pnfxr |
|
24 |
|
elicc1 |
|
25 |
22 23 24
|
mp2an |
|
26 |
25
|
simp2bi |
|
27 |
21 26
|
syl |
|
28 |
|
ltpnf |
|
29 |
16 28
|
syl |
|
30 |
|
0re |
|
31 |
|
elico2 |
|
32 |
30 23 31
|
mp2an |
|
33 |
16 27 29 32
|
syl3anbrc |
|
34 |
9 15 1 33
|
esumpfinvalf |
|
35 |
8 34
|
eqtr4d |
|
36 |
|
simpr |
|
37 |
|
nfv |
|
38 |
|
nfcv |
|
39 |
|
nfcsb1v |
|
40 |
38 39
|
nffv |
|
41 |
40
|
nfeq1 |
|
42 |
|
csbeq1a |
|
43 |
42
|
fveqeq2d |
|
44 |
37 41 43
|
cbvrexw |
|
45 |
36 44
|
sylib |
|
46 |
39
|
nfel1 |
|
47 |
42
|
eleq1d |
|
48 |
46 47
|
rspc |
|
49 |
48
|
impcom |
|
50 |
49
|
adantll |
|
51 |
|
finiunmbl |
|
52 |
51
|
adantr |
|
53 |
|
nfcv |
|
54 |
9 53 39 42
|
ssiun2sf |
|
55 |
54
|
adantl |
|
56 |
|
volss |
|
57 |
50 52 55 56
|
syl3anc |
|
58 |
57
|
3adantl3 |
|
59 |
58
|
adantlr |
|
60 |
59
|
ralrimiva |
|
61 |
|
r19.29r |
|
62 |
45 60 61
|
syl2anc |
|
63 |
|
breq1 |
|
64 |
63
|
biimpa |
|
65 |
64
|
reximi |
|
66 |
62 65
|
syl |
|
67 |
|
rexex |
|
68 |
|
19.9v |
|
69 |
67 68
|
sylib |
|
70 |
66 69
|
syl |
|
71 |
|
iccssxr |
|
72 |
18
|
ffvelrni |
|
73 |
71 72
|
sseldi |
|
74 |
51 73
|
syl |
|
75 |
74
|
3adant3 |
|
76 |
75
|
adantr |
|
77 |
|
xgepnf |
|
78 |
76 77
|
syl |
|
79 |
70 78
|
mpbid |
|
80 |
|
nfre1 |
|
81 |
13 80
|
nfan |
|
82 |
|
simpl1 |
|
83 |
20
|
3ad2antl2 |
|
84 |
83
|
adantlr |
|
85 |
81 82 84 36
|
esumpinfval |
|
86 |
79 85
|
eqtr4d |
|
87 |
|
exmid |
|
88 |
|
rexnal |
|
89 |
88
|
orbi2i |
|
90 |
87 89
|
mpbir |
|
91 |
|
r19.29 |
|
92 |
|
xrge0nre |
|
93 |
19 92
|
sylan |
|
94 |
93
|
reximi |
|
95 |
91 94
|
syl |
|
96 |
95
|
ex |
|
97 |
96
|
orim2d |
|
98 |
90 97
|
mpi |
|
99 |
98
|
3ad2ant2 |
|
100 |
35 86 99
|
mpjaodan |
|