Step |
Hyp |
Ref |
Expression |
1 |
|
mullimc.f |
|
2 |
|
mullimc.g |
|
3 |
|
mullimc.h |
|
4 |
|
mullimc.b |
|
5 |
|
mullimc.c |
|
6 |
|
mullimc.x |
|
7 |
|
mullimc.y |
|
8 |
|
limccl |
|
9 |
8 6
|
sseldi |
|
10 |
|
limccl |
|
11 |
10 7
|
sseldi |
|
12 |
9 11
|
mulcld |
|
13 |
|
simpr |
|
14 |
9
|
adantr |
|
15 |
11
|
adantr |
|
16 |
|
mulcn2 |
|
17 |
13 14 15 16
|
syl3anc |
|
18 |
4 1
|
fmptd |
|
19 |
1 4
|
dmmptd |
|
20 |
|
limcrcl |
|
21 |
6 20
|
syl |
|
22 |
21
|
simp2d |
|
23 |
19 22
|
eqsstrrd |
|
24 |
21
|
simp3d |
|
25 |
18 23 24
|
ellimc3 |
|
26 |
6 25
|
mpbid |
|
27 |
26
|
simprd |
|
28 |
27
|
r19.21bi |
|
29 |
28
|
adantrr |
|
30 |
5 2
|
fmptd |
|
31 |
30 23 24
|
ellimc3 |
|
32 |
7 31
|
mpbid |
|
33 |
32
|
simprd |
|
34 |
33
|
r19.21bi |
|
35 |
34
|
adantrl |
|
36 |
|
reeanv |
|
37 |
29 35 36
|
sylanbrc |
|
38 |
|
ifcl |
|
39 |
38
|
3ad2ant2 |
|
40 |
|
nfv |
|
41 |
|
nfv |
|
42 |
|
nfra1 |
|
43 |
|
nfra1 |
|
44 |
42 43
|
nfan |
|
45 |
40 41 44
|
nf3an |
|
46 |
|
simp11l |
|
47 |
|
simp1rl |
|
48 |
47
|
3ad2ant1 |
|
49 |
46 48
|
jca |
|
50 |
|
simp12 |
|
51 |
|
simp13l |
|
52 |
49 50 51
|
jca31 |
|
53 |
|
simp1r |
|
54 |
|
simp2 |
|
55 |
|
simp3l |
|
56 |
|
simplll |
|
57 |
56
|
3ad2ant1 |
|
58 |
|
simp1lr |
|
59 |
|
simp3r |
|
60 |
|
simp1l |
|
61 |
|
simp2 |
|
62 |
23
|
sselda |
|
63 |
60 61 62
|
syl2anc |
|
64 |
60 24
|
syl |
|
65 |
63 64
|
subcld |
|
66 |
65
|
abscld |
|
67 |
|
rpre |
|
68 |
67
|
ad2antrl |
|
69 |
68
|
3ad2ant1 |
|
70 |
|
rpre |
|
71 |
70
|
ad2antll |
|
72 |
71
|
3ad2ant1 |
|
73 |
69 72
|
ifcld |
|
74 |
|
simp3 |
|
75 |
|
min1 |
|
76 |
69 72 75
|
syl2anc |
|
77 |
66 73 69 74 76
|
ltletrd |
|
78 |
57 58 54 59 77
|
syl211anc |
|
79 |
55 78
|
jca |
|
80 |
|
rsp |
|
81 |
53 54 79 80
|
syl3c |
|
82 |
52 81
|
syld3an1 |
|
83 |
|
simp1l |
|
84 |
83 47
|
jca |
|
85 |
|
simp2 |
|
86 |
|
simp3r |
|
87 |
84 85 86
|
jca31 |
|
88 |
|
simp1r |
|
89 |
|
simp2 |
|
90 |
|
simp3l |
|
91 |
|
simplll |
|
92 |
91
|
3ad2ant1 |
|
93 |
|
simp1lr |
|
94 |
|
simp3r |
|
95 |
|
min2 |
|
96 |
69 72 95
|
syl2anc |
|
97 |
66 73 72 74 96
|
ltletrd |
|
98 |
92 93 89 94 97
|
syl211anc |
|
99 |
90 98
|
jca |
|
100 |
|
rsp |
|
101 |
88 89 99 100
|
syl3c |
|
102 |
87 101
|
syl3an1 |
|
103 |
82 102
|
jca |
|
104 |
103
|
3exp |
|
105 |
45 104
|
ralrimi |
|
106 |
|
brimralrspcev |
|
107 |
39 105 106
|
syl2anc |
|
108 |
107
|
3exp |
|
109 |
108
|
rexlimdvv |
|
110 |
37 109
|
mpd |
|
111 |
110
|
adantlr |
|
112 |
111
|
3adant3 |
|
113 |
|
nfv |
|
114 |
|
nfra1 |
|
115 |
113 114
|
nfan |
|
116 |
|
simp1l |
|
117 |
116
|
ad2antrr |
|
118 |
117
|
3ad2ant1 |
|
119 |
|
simp2 |
|
120 |
|
nfv |
|
121 |
|
nfmpt1 |
|
122 |
3 121
|
nfcxfr |
|
123 |
|
nfcv |
|
124 |
122 123
|
nffv |
|
125 |
|
nfmpt1 |
|
126 |
1 125
|
nfcxfr |
|
127 |
126 123
|
nffv |
|
128 |
|
nfcv |
|
129 |
|
nfmpt1 |
|
130 |
2 129
|
nfcxfr |
|
131 |
130 123
|
nffv |
|
132 |
127 128 131
|
nfov |
|
133 |
124 132
|
nfeq |
|
134 |
120 133
|
nfim |
|
135 |
|
eleq1w |
|
136 |
135
|
anbi2d |
|
137 |
|
fveq2 |
|
138 |
|
fveq2 |
|
139 |
|
fveq2 |
|
140 |
138 139
|
oveq12d |
|
141 |
137 140
|
eqeq12d |
|
142 |
136 141
|
imbi12d |
|
143 |
|
simpr |
|
144 |
4 5
|
mulcld |
|
145 |
3
|
fvmpt2 |
|
146 |
143 144 145
|
syl2anc |
|
147 |
1
|
fvmpt2 |
|
148 |
143 4 147
|
syl2anc |
|
149 |
148
|
eqcomd |
|
150 |
2
|
fvmpt2 |
|
151 |
143 5 150
|
syl2anc |
|
152 |
151
|
eqcomd |
|
153 |
149 152
|
oveq12d |
|
154 |
146 153
|
eqtrd |
|
155 |
134 142 154
|
chvarfv |
|
156 |
155
|
fvoveq1d |
|
157 |
118 119 156
|
syl2anc |
|
158 |
18
|
ffvelrnda |
|
159 |
30
|
ffvelrnda |
|
160 |
158 159
|
jca |
|
161 |
118 119 160
|
syl2anc |
|
162 |
|
simpll3 |
|
163 |
162
|
3ad2ant1 |
|
164 |
|
rsp |
|
165 |
164
|
3imp |
|
166 |
165
|
3adant1l |
|
167 |
|
fvoveq1 |
|
168 |
167
|
breq1d |
|
169 |
168
|
anbi1d |
|
170 |
|
oveq1 |
|
171 |
170
|
fvoveq1d |
|
172 |
171
|
breq1d |
|
173 |
169 172
|
imbi12d |
|
174 |
|
fvoveq1 |
|
175 |
174
|
breq1d |
|
176 |
175
|
anbi2d |
|
177 |
|
oveq2 |
|
178 |
177
|
fvoveq1d |
|
179 |
178
|
breq1d |
|
180 |
176 179
|
imbi12d |
|
181 |
173 180
|
rspc2v |
|
182 |
161 163 166 181
|
syl3c |
|
183 |
157 182
|
eqbrtrd |
|
184 |
183
|
3exp |
|
185 |
115 184
|
ralrimi |
|
186 |
185
|
ex |
|
187 |
186
|
reximdva |
|
188 |
112 187
|
mpd |
|
189 |
188
|
3exp |
|
190 |
189
|
rexlimdvv |
|
191 |
17 190
|
mpd |
|
192 |
191
|
ralrimiva |
|
193 |
144 3
|
fmptd |
|
194 |
193 23 24
|
ellimc3 |
|
195 |
12 192 194
|
mpbir2and |
|