Step |
Hyp |
Ref |
Expression |
1 |
|
dynkin.p |
|
2 |
|
dynkin.l |
|
3 |
|
dynkin.o |
|
4 |
|
ldgenpisys.e |
|
5 |
|
ldgenpisys.1 |
|
6 |
|
ldgenpisyslem1.1 |
|
7 |
|
ssrab2 |
|
8 |
|
pwexg |
|
9 |
|
rabexg |
|
10 |
|
elpwg |
|
11 |
3 8 9 10
|
4syl |
|
12 |
7 11
|
mpbiri |
|
13 |
|
ineq2 |
|
14 |
13
|
eleq1d |
|
15 |
|
0elpw |
|
16 |
15
|
a1i |
|
17 |
2
|
isldsys |
|
18 |
17
|
simprbi |
|
19 |
18
|
simp1d |
|
20 |
19
|
ad2antlr |
|
21 |
20
|
ex |
|
22 |
21
|
ralrimiva |
|
23 |
|
0ex |
|
24 |
23
|
elintrab |
|
25 |
22 24
|
sylibr |
|
26 |
|
in0 |
|
27 |
25 26 4
|
3eltr4g |
|
28 |
14 16 27
|
elrabd |
|
29 |
|
ineq2 |
|
30 |
29
|
eleq1d |
|
31 |
30
|
elrab |
|
32 |
|
pwidg |
|
33 |
3 32
|
syl |
|
34 |
33
|
adantr |
|
35 |
34
|
elpwdifcl |
|
36 |
2
|
pwldsys |
|
37 |
3 36
|
syl |
|
38 |
1
|
ispisys |
|
39 |
5 38
|
sylib |
|
40 |
39
|
simpld |
|
41 |
40
|
elpwid |
|
42 |
|
sseq2 |
|
43 |
42
|
intminss |
|
44 |
37 41 43
|
syl2anc |
|
45 |
4 44
|
eqsstrid |
|
46 |
45 6
|
sseldd |
|
47 |
46
|
elpwid |
|
48 |
47
|
ad3antrrr |
|
49 |
|
difin |
|
50 |
|
difin2 |
|
51 |
49 50
|
syl5eq |
|
52 |
|
incom |
|
53 |
51 52
|
eqtrdi |
|
54 |
|
difuncomp |
|
55 |
53 54
|
eqtr3d |
|
56 |
48 55
|
syl |
|
57 |
|
difeq2 |
|
58 |
57
|
eleq1d |
|
59 |
18
|
simp2d |
|
60 |
59
|
ad2antlr |
|
61 |
|
difeq2 |
|
62 |
61
|
eleq1d |
|
63 |
62
|
cbvralvw |
|
64 |
60 63
|
sylib |
|
65 |
|
simplr |
|
66 |
6 4
|
eleqtrdi |
|
67 |
|
elintrabg |
|
68 |
6 67
|
syl |
|
69 |
66 68
|
mpbid |
|
70 |
69
|
r19.21bi |
|
71 |
70
|
imp |
|
72 |
71
|
adantllr |
|
73 |
|
difeq2 |
|
74 |
73
|
eleq1d |
|
75 |
59
|
adantr |
|
76 |
|
simpr |
|
77 |
74 75 76
|
rspcdva |
|
78 |
65 72 77
|
syl2anc |
|
79 |
|
simpllr |
|
80 |
79
|
simprd |
|
81 |
80 4
|
eleqtrdi |
|
82 |
|
vex |
|
83 |
82
|
inex2 |
|
84 |
|
elintrabg |
|
85 |
83 84
|
mp1i |
|
86 |
81 85
|
mpbid |
|
87 |
|
simpr |
|
88 |
|
rspa |
|
89 |
88
|
imp |
|
90 |
86 65 87 89
|
syl21anc |
|
91 |
|
incom |
|
92 |
|
inss1 |
|
93 |
|
disjdif |
|
94 |
|
ssdisj |
|
95 |
92 93 94
|
mp2an |
|
96 |
91 95
|
eqtri |
|
97 |
96
|
a1i |
|
98 |
2 65 78 90 97
|
unelldsys |
|
99 |
58 64 98
|
rspcdva |
|
100 |
56 99
|
eqeltrd |
|
101 |
100
|
ex |
|
102 |
101
|
ralrimiva |
|
103 |
|
inex1g |
|
104 |
6 103
|
syl |
|
105 |
104
|
adantr |
|
106 |
|
elintrabg |
|
107 |
105 106
|
syl |
|
108 |
102 107
|
mpbird |
|
109 |
108 4
|
eleqtrrdi |
|
110 |
35 109
|
jca |
|
111 |
31 110
|
sylan2b |
|
112 |
|
ineq2 |
|
113 |
112
|
eleq1d |
|
114 |
113
|
elrab |
|
115 |
111 114
|
sylibr |
|
116 |
115
|
ralrimiva |
|
117 |
|
ineq2 |
|
118 |
117
|
eleq1d |
|
119 |
7
|
sspwi |
|
120 |
|
simplr |
|
121 |
119 120
|
sseldi |
|
122 |
121
|
elpwunicl |
|
123 |
|
uniin2 |
|
124 |
|
vex |
|
125 |
124
|
inex2 |
|
126 |
125
|
dfiun3 |
|
127 |
123 126
|
eqtr3i |
|
128 |
|
simplr |
|
129 |
|
nfv |
|
130 |
|
nfv |
|
131 |
|
nfdisj1 |
|
132 |
130 131
|
nfan |
|
133 |
129 132
|
nfan |
|
134 |
|
nfv |
|
135 |
133 134
|
nfan |
|
136 |
|
nfv |
|
137 |
135 136
|
nfan |
|
138 |
|
elpwi |
|
139 |
138
|
ad4antlr |
|
140 |
139
|
sselda |
|
141 |
|
ineq2 |
|
142 |
141
|
eleq1d |
|
143 |
142
|
elrab |
|
144 |
143
|
simprbi |
|
145 |
140 144
|
syl |
|
146 |
|
simpllr |
|
147 |
|
simplr |
|
148 |
4
|
eleq2i |
|
149 |
125
|
elintrab |
|
150 |
148 149
|
bitri |
|
151 |
|
rspa |
|
152 |
150 151
|
sylanb |
|
153 |
152
|
imp |
|
154 |
145 146 147 153
|
syl21anc |
|
155 |
154
|
ex |
|
156 |
137 155
|
ralrimi |
|
157 |
|
eqid |
|
158 |
157
|
rnmptss |
|
159 |
156 158
|
syl |
|
160 |
128 159
|
sselpwd |
|
161 |
|
simpllr |
|
162 |
161
|
simpld |
|
163 |
|
1stcrestlem |
|
164 |
162 163
|
syl |
|
165 |
161
|
simprd |
|
166 |
|
disjin2 |
|
167 |
|
disjrnmpt |
|
168 |
165 166 167
|
3syl |
|
169 |
|
nfmpt1 |
|
170 |
169
|
nfrn |
|
171 |
|
nfcv |
|
172 |
|
nfcv |
|
173 |
|
id |
|
174 |
170 171 172 173
|
cbvdisjf |
|
175 |
168 174
|
sylibr |
|
176 |
|
breq1 |
|
177 |
172 170
|
disjeq1f |
|
178 |
176 177
|
anbi12d |
|
179 |
|
unieq |
|
180 |
179
|
eleq1d |
|
181 |
178 180
|
imbi12d |
|
182 |
18
|
simp3d |
|
183 |
|
breq1 |
|
184 |
|
disjeq1 |
|
185 |
183 184
|
anbi12d |
|
186 |
|
unieq |
|
187 |
186
|
eleq1d |
|
188 |
185 187
|
imbi12d |
|
189 |
188
|
cbvralvw |
|
190 |
182 189
|
sylib |
|
191 |
190
|
adantr |
|
192 |
|
simpr |
|
193 |
181 191 192
|
rspcdva |
|
194 |
193
|
imp |
|
195 |
128 160 164 175 194
|
syl22anc |
|
196 |
127 195
|
eqeltrid |
|
197 |
196
|
ex |
|
198 |
197
|
ralrimiva |
|
199 |
|
vuniex |
|
200 |
199
|
inex2 |
|
201 |
200
|
elintrab |
|
202 |
198 201
|
sylibr |
|
203 |
202 4
|
eleqtrrdi |
|
204 |
118 122 203
|
elrabd |
|
205 |
204
|
ex |
|
206 |
205
|
ralrimiva |
|
207 |
28 116 206
|
3jca |
|
208 |
2
|
isldsys |
|
209 |
12 207 208
|
sylanbrc |
|