Step |
Hyp |
Ref |
Expression |
1 |
|
evlslem2.p |
|
2 |
|
evlslem2.b |
|
3 |
|
evlslem2.m |
|
4 |
|
evlslem2.z |
|
5 |
|
evlslem2.d |
|
6 |
|
evlslem2.i |
|
7 |
|
evlslem2.r |
|
8 |
|
evlslem2.s |
|
9 |
|
evlslem2.e1 |
|
10 |
|
evlslem2.e2 |
|
11 |
|
eqid |
|
12 |
|
eqid |
|
13 |
|
ovex |
|
14 |
5 13
|
rabex2 |
|
15 |
14
|
a1i |
|
16 |
|
crngring |
|
17 |
7 16
|
syl |
|
18 |
1 6 17
|
mplringd |
|
19 |
18
|
adantr |
|
20 |
|
eqid |
|
21 |
6
|
ad2antrr |
|
22 |
17
|
ad2antrr |
|
23 |
|
simprl |
|
24 |
1 20 2 5 23
|
mplelf |
|
25 |
24
|
ffvelcdmda |
|
26 |
|
simpr |
|
27 |
1 5 4 20 21 22 2 25 26
|
mplmon2cl |
|
28 |
6
|
ad2antrr |
|
29 |
17
|
ad2antrr |
|
30 |
|
simprr |
|
31 |
1 20 2 5 30
|
mplelf |
|
32 |
31
|
ffvelcdmda |
|
33 |
|
simpr |
|
34 |
1 5 4 20 28 29 2 32 33
|
mplmon2cl |
|
35 |
14
|
mptex |
|
36 |
|
funmpt |
|
37 |
|
fvex |
|
38 |
35 36 37
|
3pm3.2i |
|
39 |
38
|
a1i |
|
40 |
|
simpr |
|
41 |
7
|
adantr |
|
42 |
1 2 4 40 41
|
mplelsfi |
|
43 |
42
|
fsuppimpd |
|
44 |
1 20 2 5 40
|
mplelf |
|
45 |
|
ssidd |
|
46 |
14
|
a1i |
|
47 |
4
|
fvexi |
|
48 |
47
|
a1i |
|
49 |
44 45 46 48
|
suppssr |
|
50 |
49
|
ifeq1d |
|
51 |
|
ifid |
|
52 |
50 51
|
eqtrdi |
|
53 |
52
|
mpteq2dv |
|
54 |
|
ringgrp |
|
55 |
17 54
|
syl |
|
56 |
1 5 4 12 6 55
|
mpl0 |
|
57 |
|
fconstmpt |
|
58 |
56 57
|
eqtrdi |
|
59 |
58
|
ad2antrr |
|
60 |
53 59
|
eqtr4d |
|
61 |
60 46
|
suppss2 |
|
62 |
|
suppssfifsupp |
|
63 |
39 43 61 62
|
syl12anc |
|
64 |
63
|
ralrimiva |
|
65 |
|
fveq1 |
|
66 |
65
|
ifeq1d |
|
67 |
66
|
mpteq2dv |
|
68 |
67
|
mpteq2dv |
|
69 |
68
|
breq1d |
|
70 |
69
|
cbvralvw |
|
71 |
64 70
|
sylib |
|
72 |
71
|
r19.21bi |
|
73 |
72
|
adantrr |
|
74 |
|
equequ2 |
|
75 |
|
fveq2 |
|
76 |
74 75
|
ifbieq1d |
|
77 |
76
|
mpteq2dv |
|
78 |
77
|
cbvmptv |
|
79 |
63
|
adantrl |
|
80 |
78 79
|
eqbrtrid |
|
81 |
2 11 12 15 15 19 27 34 73 80
|
gsumdixp |
|
82 |
81
|
fveq2d |
|
83 |
|
ringcmn |
|
84 |
18 83
|
syl |
|
85 |
84
|
adantr |
|
86 |
|
crngring |
|
87 |
8 86
|
syl |
|
88 |
87
|
adantr |
|
89 |
|
ringmnd |
|
90 |
88 89
|
syl |
|
91 |
14 14
|
xpex |
|
92 |
91
|
a1i |
|
93 |
|
ghmmhm |
|
94 |
9 93
|
syl |
|
95 |
94
|
adantr |
|
96 |
18
|
ad2antrr |
|
97 |
27
|
adantrr |
|
98 |
34
|
adantrl |
|
99 |
2 11
|
ringcl |
|
100 |
96 97 98 99
|
syl3anc |
|
101 |
100
|
ralrimivva |
|
102 |
|
eqid |
|
103 |
102
|
fmpo |
|
104 |
101 103
|
sylib |
|
105 |
14 14
|
mpoex |
|
106 |
102
|
mpofun |
|
107 |
105 106 37
|
3pm3.2i |
|
108 |
107
|
a1i |
|
109 |
73
|
fsuppimpd |
|
110 |
80
|
fsuppimpd |
|
111 |
|
xpfi |
|
112 |
109 110 111
|
syl2anc |
|
113 |
2 12 11 19 27 34 15 15
|
evlslem4 |
|
114 |
|
suppssfifsupp |
|
115 |
108 112 113 114
|
syl12anc |
|
116 |
2 12 85 90 92 95 104 115
|
gsummhm |
|
117 |
6
|
ad2antrr |
|
118 |
7
|
ad2antrr |
|
119 |
|
eqid |
|
120 |
|
simprl |
|
121 |
|
simprr |
|
122 |
25
|
adantrr |
|
123 |
32
|
adantrl |
|
124 |
1 5 4 20 117 118 11 119 120 121 122 123
|
mplmon2mul |
|
125 |
124
|
fveq2d |
|
126 |
10
|
anassrs |
|
127 |
125 126
|
eqtrd |
|
128 |
127
|
3impb |
|
129 |
128
|
mpoeq3dva |
|
130 |
129
|
oveq2d |
|
131 |
|
eqidd |
|
132 |
|
eqid |
|
133 |
2 132
|
ghmf |
|
134 |
9 133
|
syl |
|
135 |
134
|
feqmptd |
|
136 |
135
|
adantr |
|
137 |
|
fveq2 |
|
138 |
100 131 136 137
|
fmpoco |
|
139 |
138
|
oveq2d |
|
140 |
|
eqidd |
|
141 |
|
fveq2 |
|
142 |
27 140 136 141
|
fmptco |
|
143 |
142
|
oveq2d |
|
144 |
|
eqidd |
|
145 |
|
fveq2 |
|
146 |
34 144 136 145
|
fmptco |
|
147 |
146
|
oveq2d |
|
148 |
143 147
|
oveq12d |
|
149 |
|
eqid |
|
150 |
134
|
ad2antrr |
|
151 |
150 27
|
ffvelcdmd |
|
152 |
134
|
ad2antrr |
|
153 |
152 34
|
ffvelcdmd |
|
154 |
14
|
mptex |
|
155 |
|
funmpt |
|
156 |
|
fvex |
|
157 |
154 155 156
|
3pm3.2i |
|
158 |
157
|
a1i |
|
159 |
|
ssidd |
|
160 |
12 149
|
ghmid |
|
161 |
9 160
|
syl |
|
162 |
14
|
mptex |
|
163 |
162
|
a1i |
|
164 |
37
|
a1i |
|
165 |
159 161 163 164
|
suppssfv |
|
166 |
165
|
adantr |
|
167 |
|
suppssfifsupp |
|
168 |
158 109 166 167
|
syl12anc |
|
169 |
14
|
mptex |
|
170 |
|
funmpt |
|
171 |
169 170 156
|
3pm3.2i |
|
172 |
171
|
a1i |
|
173 |
|
ssidd |
|
174 |
14
|
mptex |
|
175 |
174
|
a1i |
|
176 |
173 161 175 164
|
suppssfv |
|
177 |
176
|
adantr |
|
178 |
|
suppssfifsupp |
|
179 |
172 110 177 178
|
syl12anc |
|
180 |
132 3 149 15 15 88 151 153 168 179
|
gsumdixp |
|
181 |
148 180
|
eqtrd |
|
182 |
130 139 181
|
3eqtr4d |
|
183 |
82 116 182
|
3eqtr2d |
|
184 |
6
|
adantr |
|
185 |
17
|
adantr |
|
186 |
1 5 4 2 184 185 23
|
mplcoe4 |
|
187 |
1 5 4 2 184 185 30
|
mplcoe4 |
|
188 |
186 187
|
oveq12d |
|
189 |
188
|
fveq2d |
|
190 |
186
|
fveq2d |
|
191 |
27
|
fmpttd |
|
192 |
2 12 85 90 15 95 191 73
|
gsummhm |
|
193 |
190 192
|
eqtr4d |
|
194 |
187
|
fveq2d |
|
195 |
34
|
fmpttd |
|
196 |
2 12 85 90 15 95 195 80
|
gsummhm |
|
197 |
194 196
|
eqtr4d |
|
198 |
193 197
|
oveq12d |
|
199 |
183 189 198
|
3eqtr4d |
|