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