Step |
Hyp |
Ref |
Expression |
1 |
|
mnringmulrcld.2 |
Could not format F = ( R MndRing M ) : No typesetting found for |- F = ( R MndRing M ) with typecode |- |
2 |
|
mnringmulrcld.3 |
|
3 |
|
mnringmulrcld.1 |
|
4 |
|
mnringmulrcld.4 |
|
5 |
|
mnringmulrcld.5 |
|
6 |
|
mnringmulrcld.6 |
|
7 |
|
mnringmulrcld.7 |
|
8 |
|
mnringmulrcld.8 |
|
9 |
|
eqid |
|
10 |
|
eqid |
|
11 |
|
eqid |
|
12 |
1 2 9 10 3 11 4 5 6 7 8
|
mnringmulrvald |
|
13 |
|
eqid |
|
14 |
1 5 6
|
mnringlmodd |
|
15 |
|
lmodcmn |
|
16 |
14 15
|
syl |
|
17 |
3
|
fvexi |
|
18 |
17 17
|
xpex |
|
19 |
18
|
a1i |
|
20 |
5
|
3ad2ant1 |
|
21 |
|
eqid |
|
22 |
1 2 3 21 5 6 7
|
mnringbasefd |
|
23 |
22
|
3ad2ant1 |
|
24 |
|
simp2 |
|
25 |
23 24
|
ffvelrnd |
|
26 |
1 2 3 21 5 6 8
|
mnringbasefd |
|
27 |
26
|
3ad2ant1 |
|
28 |
|
simp3 |
|
29 |
27 28
|
ffvelrnd |
|
30 |
21 9
|
ringcl |
|
31 |
20 25 29 30
|
syl3anc |
|
32 |
21 10
|
ring0cl |
|
33 |
20 32
|
syl |
|
34 |
31 33
|
ifcld |
|
35 |
34
|
adantr |
|
36 |
35
|
fmpttd |
|
37 |
21
|
fvexi |
|
38 |
37 17
|
elmap |
|
39 |
36 38
|
sylibr |
|
40 |
17
|
a1i |
|
41 |
|
eqid |
|
42 |
40 33 41
|
sniffsupp |
|
43 |
39 42
|
jca |
|
44 |
6
|
3ad2ant1 |
|
45 |
1 2 3 21 10 20 44
|
mnringelbased |
|
46 |
43 45
|
mpbird |
|
47 |
46
|
3expb |
|
48 |
47
|
ralrimivva |
|
49 |
|
eqid |
|
50 |
49
|
fmpo |
|
51 |
48 50
|
sylib |
|
52 |
17 17
|
mpoex |
|
53 |
52
|
a1i |
|
54 |
51
|
ffnd |
|
55 |
13
|
fvexi |
|
56 |
55
|
a1i |
|
57 |
1 2 10 5 6 7
|
mnringbasefsuppd |
|
58 |
57
|
fsuppimpd |
|
59 |
1 2 10 5 6 8
|
mnringbasefsuppd |
|
60 |
59
|
fsuppimpd |
|
61 |
|
xpfi |
|
62 |
58 60 61
|
syl2anc |
|
63 |
|
elxpi |
|
64 |
|
simpl |
|
65 |
64
|
2eximi |
|
66 |
63 65
|
syl |
|
67 |
66
|
adantl |
|
68 |
|
nfv |
|
69 |
|
nfv |
|
70 |
|
nfmpo1 |
|
71 |
|
nfcv |
|
72 |
70 71
|
nffv |
|
73 |
|
nfcv |
|
74 |
72 73
|
nfeq |
|
75 |
69 74
|
nfor |
|
76 |
|
nfv |
|
77 |
|
nfv |
|
78 |
|
nfmpo2 |
|
79 |
|
nfcv |
|
80 |
78 79
|
nffv |
|
81 |
|
nfcv |
|
82 |
80 81
|
nfeq |
|
83 |
77 82
|
nfor |
|
84 |
|
simp3 |
|
85 |
|
simp2 |
|
86 |
84 85
|
eqeltrrd |
|
87 |
|
opelxp |
|
88 |
86 87
|
sylib |
|
89 |
|
ianor |
|
90 |
22
|
ffnd |
|
91 |
17
|
a1i |
|
92 |
10
|
fvexi |
|
93 |
92
|
a1i |
|
94 |
|
elsuppfn |
|
95 |
90 91 93 94
|
syl3anc |
|
96 |
95
|
biimprd |
|
97 |
96
|
3ad2ant1 |
|
98 |
24 97
|
mpand |
|
99 |
98
|
necon1bd |
|
100 |
26
|
ffnd |
|
101 |
|
elsuppfn |
|
102 |
100 91 93 101
|
syl3anc |
|
103 |
102
|
biimprd |
|
104 |
103
|
3ad2ant1 |
|
105 |
28 104
|
mpand |
|
106 |
105
|
necon1bd |
|
107 |
99 106
|
orim12d |
|
108 |
107
|
imp |
|
109 |
89 108
|
sylan2b |
|
110 |
|
oveq1 |
|
111 |
21 9 10
|
ringlz |
|
112 |
20 29 111
|
syl2anc |
|
113 |
110 112
|
sylan9eqr |
|
114 |
|
oveq2 |
|
115 |
21 9 10
|
ringrz |
|
116 |
20 25 115
|
syl2anc |
|
117 |
114 116
|
sylan9eqr |
|
118 |
113 117
|
jaodan |
|
119 |
118
|
adantr |
|
120 |
|
eqidd |
|
121 |
119 120
|
ifeqda |
|
122 |
121
|
mpteq2dv |
|
123 |
|
fconstmpt |
|
124 |
1 10 3 5 6
|
mnring0g2d |
|
125 |
123 124
|
syl5eqr |
|
126 |
125
|
3ad2ant1 |
|
127 |
126
|
adantr |
|
128 |
122 127
|
eqtrd |
|
129 |
109 128
|
syldan |
|
130 |
129
|
ex |
|
131 |
130
|
orrd |
|
132 |
131
|
3expb |
|
133 |
132
|
3adant3 |
|
134 |
|
eleq1 |
|
135 |
|
opelxp |
|
136 |
134 135
|
syl6bb |
|
137 |
136
|
3ad2ant3 |
|
138 |
|
simp2l |
|
139 |
|
simp2r |
|
140 |
|
eqidd |
|
141 |
|
simp3 |
|
142 |
17
|
mptex |
|
143 |
142
|
a1i |
|
144 |
140 141 143
|
fvmpopr2d |
|
145 |
138 139 144
|
mpd3an23 |
|
146 |
145
|
eqeq1d |
|
147 |
137 146
|
orbi12d |
|
148 |
133 147
|
mpbird |
|
149 |
88 148
|
syld3an2 |
|
150 |
149
|
3expia |
|
151 |
76 83 150
|
exlimd |
|
152 |
68 75 151
|
exlimd |
|
153 |
67 152
|
mpd |
|
154 |
53 54 56 62 153
|
finnzfsuppd |
|
155 |
2 13 16 19 51 154
|
gsumcl |
|
156 |
12 155
|
eqeltrd |
|