Step |
Hyp |
Ref |
Expression |
1 |
|
sge0fodjrnlem.k |
|
2 |
|
sge0fodjrnlem.n |
|
3 |
|
sge0fodjrnlem.bd |
|
4 |
|
sge0fodjrnlem.c |
|
5 |
|
sge0fodjrnlem.f |
|
6 |
|
sge0fodjrnlem.dj |
|
7 |
|
sge0fodjrnlem.fng |
|
8 |
|
sge0fodjrnlem.b |
|
9 |
|
sge0fodjrnlem.b0 |
|
10 |
|
sge0fodjrnlem.z |
|
11 |
|
fornex |
|
12 |
4 5 11
|
sylc |
|
13 |
|
difssd |
|
14 |
|
simpl |
|
15 |
13
|
sselda |
|
16 |
14 15 8
|
syl2anc |
|
17 |
|
simpl |
|
18 |
|
dfin4 |
|
19 |
18
|
eqcomi |
|
20 |
|
inss2 |
|
21 |
19 20
|
eqsstri |
|
22 |
|
id |
|
23 |
21 22
|
sseldi |
|
24 |
|
elsni |
|
25 |
23 24
|
syl |
|
26 |
25
|
adantl |
|
27 |
17 26 9
|
syl2anc |
|
28 |
1 12 13 16 27
|
sge0ss |
|
29 |
28
|
eqcomd |
|
30 |
|
difexg |
|
31 |
4 30
|
syl |
|
32 |
|
eqid |
|
33 |
|
fof |
|
34 |
5 33
|
syl |
|
35 |
34
|
ffvelrnda |
|
36 |
|
fveq2 |
|
37 |
36
|
neeq1d |
|
38 |
37
|
cbvrabv |
|
39 |
36
|
cbvmptv |
|
40 |
39
|
rneqi |
|
41 |
40
|
difeq1i |
|
42 |
2 32 35 6 38 41
|
disjf1o |
|
43 |
34
|
feqmptd |
|
44 |
|
difssd |
|
45 |
44
|
sselda |
|
46 |
|
eldifi |
|
47 |
46
|
adantr |
|
48 |
|
id |
|
49 |
|
fvex |
|
50 |
49
|
elsn |
|
51 |
48 50
|
sylibr |
|
52 |
51
|
adantl |
|
53 |
47 52
|
jca |
|
54 |
53
|
adantll |
|
55 |
34
|
ffnd |
|
56 |
|
elpreima |
|
57 |
55 56
|
syl |
|
58 |
57
|
ad2antrr |
|
59 |
54 58
|
mpbird |
|
60 |
59 10
|
eleqtrrdi |
|
61 |
|
eldifn |
|
62 |
61
|
ad2antlr |
|
63 |
60 62
|
pm2.65da |
|
64 |
63
|
neqned |
|
65 |
45 64
|
jca |
|
66 |
37
|
elrab |
|
67 |
65 66
|
sylibr |
|
68 |
67
|
ex |
|
69 |
66
|
simplbi |
|
70 |
69
|
adantl |
|
71 |
10
|
eleq2i |
|
72 |
71
|
biimpi |
|
73 |
72
|
adantl |
|
74 |
57
|
adantr |
|
75 |
73 74
|
mpbid |
|
76 |
75
|
simprd |
|
77 |
|
elsni |
|
78 |
76 77
|
syl |
|
79 |
78
|
adantlr |
|
80 |
66
|
simprbi |
|
81 |
80
|
ad2antlr |
|
82 |
81
|
neneqd |
|
83 |
79 82
|
pm2.65da |
|
84 |
70 83
|
eldifd |
|
85 |
84
|
ex |
|
86 |
2 85
|
ralrimi |
|
87 |
|
dfss3 |
|
88 |
86 87
|
sylibr |
|
89 |
88
|
sseld |
|
90 |
68 89
|
impbid |
|
91 |
2 90
|
alrimi |
|
92 |
|
dfcleq |
|
93 |
91 92
|
sylibr |
|
94 |
43 93
|
reseq12d |
|
95 |
43 39
|
eqtr4di |
|
96 |
95
|
eqcomd |
|
97 |
96
|
rneqd |
|
98 |
|
forn |
|
99 |
5 98
|
syl |
|
100 |
97 99
|
eqtr2d |
|
101 |
100
|
difeq1d |
|
102 |
94 93 101
|
f1oeq123d |
|
103 |
42 102
|
mpbird |
|
104 |
|
fvres |
|
105 |
104
|
adantl |
|
106 |
|
simpl |
|
107 |
106 45 7
|
syl2anc |
|
108 |
105 107
|
eqtrd |
|
109 |
1 2 3 31 103 108 16
|
sge0f1o |
|
110 |
7
|
eqcomd |
|
111 |
110 35
|
eqeltrd |
|
112 |
106 45 111
|
syl2anc |
|
113 |
112
|
ex |
|
114 |
113
|
imdistani |
|
115 |
|
nfcv |
|
116 |
|
nfv |
|
117 |
1 116
|
nfan |
|
118 |
|
nfv |
|
119 |
117 118
|
nfim |
|
120 |
|
eleq1 |
|
121 |
120
|
anbi2d |
|
122 |
3
|
eleq1d |
|
123 |
121 122
|
imbi12d |
|
124 |
115 119 123 8
|
vtoclgf |
|
125 |
112 114 124
|
sylc |
|
126 |
|
simpl |
|
127 |
|
eldifi |
|
128 |
127
|
adantl |
|
129 |
126 128 111
|
syl2anc |
|
130 |
|
dfin4 |
|
131 |
|
difss |
|
132 |
130 131
|
eqsstri |
|
133 |
|
inss2 |
|
134 |
|
id |
|
135 |
|
dfin4 |
|
136 |
135
|
eqcomi |
|
137 |
134 136
|
eleqtrdi |
|
138 |
133 137
|
sseldi |
|
139 |
138 127
|
elind |
|
140 |
132 139
|
sseldi |
|
141 |
140
|
adantl |
|
142 |
78
|
eqcomd |
|
143 |
|
simpl |
|
144 |
75
|
simpld |
|
145 |
143 144 7
|
syl2anc |
|
146 |
142 145
|
eqtr2d |
|
147 |
126 141 146
|
syl2anc |
|
148 |
126 147
|
jca |
|
149 |
|
nfv |
|
150 |
1 149
|
nfan |
|
151 |
|
nfv |
|
152 |
150 151
|
nfim |
|
153 |
|
eqeq1 |
|
154 |
153
|
anbi2d |
|
155 |
3
|
eqeq1d |
|
156 |
154 155
|
imbi12d |
|
157 |
115 152 156 9
|
vtoclgf |
|
158 |
129 148 157
|
sylc |
|
159 |
2 4 44 125 158
|
sge0ss |
|
160 |
29 109 159
|
3eqtrd |
|