Step |
Hyp |
Ref |
Expression |
1 |
|
voliunsge0lem.s |
|
2 |
|
voliunsge0lem.g |
|
3 |
|
voliunsge0lem.e |
|
4 |
|
voliunsge0lem.d |
|
5 |
|
nfv |
|
6 |
|
nfcv |
|
7 |
|
nfiu1 |
|
8 |
6 7
|
nffv |
|
9 |
8
|
nfeq1 |
|
10 |
|
iccssxr |
|
11 |
|
volf |
|
12 |
11
|
a1i |
|
13 |
3
|
ffvelrnda |
|
14 |
13
|
ralrimiva |
|
15 |
|
iunmbl |
|
16 |
14 15
|
syl |
|
17 |
12 16
|
ffvelrnd |
|
18 |
10 17
|
sseldi |
|
19 |
18
|
adantr |
|
20 |
19
|
3adant3 |
|
21 |
|
id |
|
22 |
21
|
eqcomd |
|
23 |
22
|
3ad2ant3 |
|
24 |
16
|
adantr |
|
25 |
|
ssiun2 |
|
26 |
25
|
adantl |
|
27 |
|
volss |
|
28 |
13 24 26 27
|
syl3anc |
|
29 |
28
|
3adant3 |
|
30 |
23 29
|
eqbrtrd |
|
31 |
20 30
|
xrgepnfd |
|
32 |
31
|
3exp |
|
33 |
5 9 32
|
rexlimd |
|
34 |
33
|
imp |
|
35 |
|
nfre1 |
|
36 |
5 35
|
nfan |
|
37 |
|
nnex |
|
38 |
37
|
a1i |
|
39 |
11
|
a1i |
|
40 |
39 13
|
ffvelrnd |
|
41 |
40
|
adantlr |
|
42 |
|
simpr |
|
43 |
36 38 41 42
|
sge0pnfmpt |
|
44 |
34 43
|
eqtr4d |
|
45 |
|
ralnex |
|
46 |
45
|
biimpri |
|
47 |
46
|
adantl |
|
48 |
40
|
adantr |
|
49 |
21
|
necon3bi |
|
50 |
49
|
adantl |
|
51 |
|
ge0xrre |
|
52 |
48 50 51
|
syl2anc |
|
53 |
52
|
ex |
|
54 |
|
renepnf |
|
55 |
54
|
neneqd |
|
56 |
55
|
a1i |
|
57 |
53 56
|
impbid |
|
58 |
57
|
ralbidva |
|
59 |
58
|
adantr |
|
60 |
47 59
|
mpbid |
|
61 |
|
nfra1 |
|
62 |
5 61
|
nfan |
|
63 |
13
|
adantlr |
|
64 |
|
rspa |
|
65 |
64
|
adantll |
|
66 |
63 65
|
jca |
|
67 |
66
|
ex |
|
68 |
62 67
|
ralrimi |
|
69 |
4
|
adantr |
|
70 |
1 2
|
voliun |
|
71 |
68 69 70
|
syl2anc |
|
72 |
|
1zzd |
|
73 |
|
nnuz |
|
74 |
|
nfv |
|
75 |
62 74
|
nfan |
|
76 |
|
nfv |
|
77 |
75 76
|
nfim |
|
78 |
|
eleq1w |
|
79 |
78
|
anbi2d |
|
80 |
|
2fveq3 |
|
81 |
80
|
eleq1d |
|
82 |
79 81
|
imbi12d |
|
83 |
|
0xr |
|
84 |
83
|
a1i |
|
85 |
|
pnfxr |
|
86 |
85
|
a1i |
|
87 |
65
|
rexrd |
|
88 |
|
volge0 |
|
89 |
13 88
|
syl |
|
90 |
89
|
adantlr |
|
91 |
65
|
ltpnfd |
|
92 |
84 86 87 90 91
|
elicod |
|
93 |
77 82 92
|
chvarfv |
|
94 |
80
|
cbvmptv |
|
95 |
93 94
|
fmptd |
|
96 |
|
seqeq3 |
|
97 |
2 96
|
ax-mp |
|
98 |
1 97
|
eqtri |
|
99 |
72 73 95 98
|
sge0seq |
|
100 |
71 99
|
eqtr4d |
|
101 |
60 100
|
syldan |
|
102 |
44 101
|
pm2.61dan |
|