Step |
Hyp |
Ref |
Expression |
1 |
|
zartop.1 |
Could not format S = ( Spec ` R ) : No typesetting found for |- S = ( Spec ` R ) with typecode |- |
2 |
|
zartop.2 |
|
3 |
|
zarcmplem.1 |
Could not format V = ( i e. ( LIdeal ` R ) |-> { j e. ( PrmIdeal ` R ) | i C_ j } ) : No typesetting found for |- V = ( i e. ( LIdeal ` R ) |-> { j e. ( PrmIdeal ` R ) | i C_ j } ) with typecode |- |
4 |
|
crngring |
|
5 |
|
eqid |
|
6 |
1 2 5
|
zar0ring |
|
7 |
4 6
|
sylan |
|
8 |
|
0cmp |
|
9 |
7 8
|
eqeltrdi |
|
10 |
1 2
|
zartop |
|
11 |
|
fvex |
|
12 |
11
|
mptex |
Could not format ( i e. ( LIdeal ` R ) |-> { j e. ( PrmIdeal ` R ) | i C_ j } ) e. _V : No typesetting found for |- ( i e. ( LIdeal ` R ) |-> { j e. ( PrmIdeal ` R ) | i C_ j } ) e. _V with typecode |- |
13 |
3 12
|
eqeltri |
|
14 |
|
imaexg |
|
15 |
13 14
|
mp1i |
|
16 |
|
suppssdm |
|
17 |
|
imass2 |
|
18 |
16 17
|
mp1i |
|
19 |
3
|
funmpt2 |
|
20 |
|
ssidd |
|
21 |
|
simpllr |
|
22 |
|
fvexd |
|
23 |
13
|
cnvex |
|
24 |
23
|
imaex |
|
25 |
24
|
a1i |
|
26 |
22 25
|
elmapd |
|
27 |
21 26
|
mpbid |
|
28 |
27
|
fdmd |
|
29 |
28
|
adantr |
|
30 |
20 29
|
sseqtrd |
|
31 |
|
funimass2 |
|
32 |
19 30 31
|
sylancr |
|
33 |
18 32
|
sstrd |
|
34 |
15 33
|
elpwd |
|
35 |
|
simpllr |
|
36 |
35
|
fsuppimpd |
|
37 |
|
imafi |
|
38 |
19 36 37
|
sylancr |
|
39 |
34 38
|
elind |
|
40 |
|
inteq |
|
41 |
40
|
eqeq2d |
|
42 |
41
|
adantl |
|
43 |
16 29
|
sseqtrid |
|
44 |
|
cnvimass |
|
45 |
43 44
|
sstrdi |
|
46 |
|
intimafv |
|
47 |
19 45 46
|
sylancr |
|
48 |
|
simplll |
|
49 |
48
|
crngringd |
|
50 |
49
|
ad4antr |
|
51 |
|
fvex |
Could not format ( PrmIdeal ` R ) e. _V : No typesetting found for |- ( PrmIdeal ` R ) e. _V with typecode |- |
52 |
51
|
rabex |
Could not format { j e. ( PrmIdeal ` R ) | i C_ j } e. _V : No typesetting found for |- { j e. ( PrmIdeal ` R ) | i C_ j } e. _V with typecode |- |
53 |
52 3
|
dmmpti |
|
54 |
45 53
|
sseqtrdi |
|
55 |
|
simp-7r |
|
56 |
|
simpllr |
|
57 |
|
eqid |
|
58 |
|
ringcmn |
|
59 |
4 58
|
syl |
|
60 |
59
|
ad8antr |
|
61 |
24
|
a1i |
|
62 |
27
|
ad2antrr |
|
63 |
|
simpr |
|
64 |
|
ssidd |
|
65 |
63 64
|
eqsstrd |
|
66 |
35
|
adantr |
|
67 |
5 57 60 61 62 65 66
|
gsumres |
|
68 |
|
res0 |
|
69 |
68
|
oveq2i |
|
70 |
57
|
gsum0 |
|
71 |
69 70
|
eqtri |
|
72 |
67 71
|
eqtr3di |
|
73 |
56 72
|
eqtr2d |
|
74 |
|
eqid |
|
75 |
5 57 74
|
01eq0ring |
|
76 |
50 73 75
|
syl2an2r |
|
77 |
76
|
fveq2d |
|
78 |
|
fvex |
|
79 |
|
hashsng |
|
80 |
78 79
|
ax-mp |
|
81 |
77 80
|
eqtrdi |
|
82 |
55 81
|
mteqand |
|
83 |
|
eqid |
|
84 |
3 83
|
zarclsiin |
|
85 |
50 54 82 84
|
syl3anc |
|
86 |
|
nfv |
|
87 |
|
nfra1 |
|
88 |
86 87
|
nfan |
|
89 |
54
|
sselda |
|
90 |
|
eqid |
|
91 |
5 90
|
lidlss |
|
92 |
89 91
|
syl |
|
93 |
92
|
ex |
|
94 |
88 93
|
ralrimi |
|
95 |
|
unissb |
|
96 |
94 95
|
sylibr |
|
97 |
83 5 90
|
rspcl |
|
98 |
50 96 97
|
syl2anc |
|
99 |
5 90
|
lidlss |
|
100 |
98 99
|
syl |
|
101 |
83 5 74
|
rsp1 |
|
102 |
50 101
|
syl |
|
103 |
27
|
adantr |
|
104 |
103 43
|
fssresd |
|
105 |
|
fvex |
|
106 |
|
ovex |
|
107 |
105 106
|
elmap |
|
108 |
104 107
|
sylibr |
|
109 |
|
breq1 |
|
110 |
|
oveq2 |
|
111 |
110
|
eqeq2d |
|
112 |
|
fveq1 |
|
113 |
112
|
eleq1d |
|
114 |
113
|
ralbidv |
|
115 |
109 111 114
|
3anbi123d |
|
116 |
115
|
adantl |
|
117 |
|
fvexd |
|
118 |
35 117
|
fsuppres |
|
119 |
|
simplr |
|
120 |
50 58
|
syl |
|
121 |
24
|
a1i |
|
122 |
|
ssidd |
|
123 |
5 57 120 121 103 122 35
|
gsumres |
|
124 |
119 123
|
eqtr4d |
|
125 |
|
simpr |
|
126 |
125
|
fvresd |
|
127 |
16 28
|
sseqtrid |
|
128 |
127
|
sselda |
|
129 |
|
fveq2 |
|
130 |
|
id |
|
131 |
129 130
|
eleq12d |
|
132 |
131
|
adantl |
|
133 |
128 132
|
rspcdv |
|
134 |
133
|
imp |
|
135 |
134
|
an32s |
|
136 |
126 135
|
eqeltrd |
|
137 |
136
|
ralrimiva |
|
138 |
118 124 137
|
3jca |
|
139 |
108 116 138
|
rspcedvd |
|
140 |
|
eqid |
|
141 |
83 5 57 140 50 54
|
elrspunidl |
|
142 |
139 141
|
mpbird |
|
143 |
142
|
snssd |
|
144 |
83 90
|
rspssp |
|
145 |
50 98 143 144
|
syl3anc |
|
146 |
102 145
|
eqsstrrd |
|
147 |
100 146
|
eqssd |
|
148 |
147
|
fveq2d |
|
149 |
90 5
|
lidl1 |
|
150 |
4 149
|
syl |
|
151 |
3 5
|
zarcls1 |
|
152 |
150 151
|
mpdan |
|
153 |
5 152
|
mpbiri |
|
154 |
153
|
ad7antr |
|
155 |
148 154
|
eqtrd |
|
156 |
47 85 155
|
3eqtrrd |
|
157 |
39 42 156
|
rspcedvd |
|
158 |
157
|
exp41 |
|
159 |
158
|
3imp2 |
|
160 |
5 74
|
ringidcl |
|
161 |
49 160
|
syl |
|
162 |
|
simplr |
|
163 |
|
eqid |
Could not format ( PrmIdeal ` R ) = ( PrmIdeal ` R ) : No typesetting found for |- ( PrmIdeal ` R ) = ( PrmIdeal ` R ) with typecode |- |
164 |
1 2 163 3
|
zartopn |
Could not format ( R e. CRing -> ( J e. ( TopOn ` ( PrmIdeal ` R ) ) /\ ran V = ( Clsd ` J ) ) ) : No typesetting found for |- ( R e. CRing -> ( J e. ( TopOn ` ( PrmIdeal ` R ) ) /\ ran V = ( Clsd ` J ) ) ) with typecode |- |
165 |
164
|
simprd |
|
166 |
48 165
|
syl |
|
167 |
166
|
pweqd |
|
168 |
162 167
|
eleqtrrd |
|
169 |
168
|
elpwid |
|
170 |
|
intimafv |
|
171 |
19 44 170
|
mp2an |
|
172 |
|
funimacnv |
|
173 |
19 172
|
ax-mp |
|
174 |
|
df-ss |
|
175 |
174
|
biimpi |
|
176 |
173 175
|
syl5eq |
|
177 |
176
|
inteqd |
|
178 |
171 177
|
eqtr3id |
|
179 |
169 178
|
syl |
|
180 |
44
|
a1i |
|
181 |
180 53
|
sseqtrdi |
|
182 |
19
|
a1i |
|
183 |
|
inteq |
|
184 |
|
int0 |
|
185 |
183 184
|
eqtrdi |
|
186 |
|
vn0 |
|
187 |
|
neeq1 |
|
188 |
186 187
|
mpbiri |
|
189 |
185 188
|
syl |
|
190 |
189
|
necon2i |
|
191 |
190
|
adantl |
|
192 |
|
preiman0 |
|
193 |
182 169 191 192
|
syl3anc |
|
194 |
3 83
|
zarclsiin |
|
195 |
49 181 193 194
|
syl3anc |
|
196 |
|
simpr |
|
197 |
179 195 196
|
3eqtr3d |
|
198 |
181
|
sselda |
|
199 |
198 91
|
syl |
|
200 |
199
|
ralrimiva |
|
201 |
|
unissb |
|
202 |
200 201
|
sylibr |
|
203 |
83 5 90
|
rspcl |
|
204 |
49 202 203
|
syl2anc |
|
205 |
3 5
|
zarcls1 |
|
206 |
48 204 205
|
syl2anc |
|
207 |
197 206
|
mpbid |
|
208 |
161 207
|
eleqtrrd |
|
209 |
83 5 57 140 49 181
|
elrspunidl |
|
210 |
208 209
|
mpbid |
|
211 |
159 210
|
r19.29a |
|
212 |
|
0ex |
|
213 |
|
vex |
|
214 |
|
elfi |
|
215 |
212 213 214
|
mp2an |
|
216 |
211 215
|
sylibr |
|
217 |
216
|
ex |
|
218 |
217
|
necon3bd |
|
219 |
218
|
ralrimiva |
|
220 |
|
cmpfi |
|
221 |
220
|
biimpar |
|
222 |
10 219 221
|
syl2an2r |
|
223 |
9 222
|
pm2.61dane |
|