Step |
Hyp |
Ref |
Expression |
1 |
|
frlmsslsp.y |
|
2 |
|
frlmsslsp.u |
|
3 |
|
frlmsslsp.k |
|
4 |
|
frlmsslsp.b |
|
5 |
|
frlmsslsp.z |
|
6 |
|
frlmsslsp.c |
|
7 |
1
|
frlmlmod |
|
8 |
7
|
3adant3 |
|
9 |
|
eqid |
|
10 |
1 9 4 5 6
|
frlmsslss2 |
|
11 |
2 1 4
|
uvcff |
|
12 |
11
|
3adant3 |
|
13 |
12
|
adantr |
|
14 |
|
simp3 |
|
15 |
14
|
sselda |
|
16 |
13 15
|
ffvelrnd |
|
17 |
|
simpl2 |
|
18 |
|
eqid |
|
19 |
1 18 4
|
frlmbasf |
|
20 |
17 16 19
|
syl2anc |
|
21 |
|
simpll1 |
|
22 |
|
simpll2 |
|
23 |
15
|
adantr |
|
24 |
|
eldifi |
|
25 |
24
|
adantl |
|
26 |
|
elneeldif |
|
27 |
26
|
adantll |
|
28 |
2 21 22 23 25 27 5
|
uvcvv0 |
|
29 |
20 28
|
suppss |
|
30 |
|
oveq1 |
|
31 |
30
|
sseq1d |
|
32 |
31 6
|
elrab2 |
|
33 |
16 29 32
|
sylanbrc |
|
34 |
33
|
ralrimiva |
|
35 |
12
|
ffund |
|
36 |
12
|
fdmd |
|
37 |
14 36
|
sseqtrrd |
|
38 |
|
funimass4 |
|
39 |
35 37 38
|
syl2anc |
|
40 |
34 39
|
mpbird |
|
41 |
9 3
|
lspssp |
|
42 |
8 10 40 41
|
syl3anc |
|
43 |
|
simpl1 |
|
44 |
|
simpl2 |
|
45 |
6
|
ssrab3 |
|
46 |
45
|
a1i |
|
47 |
46
|
sselda |
|
48 |
|
eqid |
|
49 |
2 1 4 48
|
uvcresum |
|
50 |
43 44 47 49
|
syl3anc |
|
51 |
|
eqid |
|
52 |
|
lmodabl |
|
53 |
8 52
|
syl |
|
54 |
53
|
adantr |
|
55 |
|
imassrn |
|
56 |
12
|
frnd |
|
57 |
55 56
|
sstrid |
|
58 |
4 9 3
|
lspcl |
|
59 |
8 57 58
|
syl2anc |
|
60 |
9
|
lsssubg |
|
61 |
8 59 60
|
syl2anc |
|
62 |
61
|
adantr |
|
63 |
1 18 4
|
frlmbasf |
|
64 |
63
|
3ad2antl2 |
|
65 |
64
|
ffnd |
|
66 |
12
|
ffnd |
|
67 |
66
|
adantr |
|
68 |
|
simpl2 |
|
69 |
|
inidm |
|
70 |
65 67 68 68 69
|
offn |
|
71 |
47 70
|
syldan |
|
72 |
47 65
|
syldan |
|
73 |
72
|
adantrr |
|
74 |
66
|
adantr |
|
75 |
|
simpl2 |
|
76 |
|
simprr |
|
77 |
|
fnfvof |
|
78 |
73 74 75 76 77
|
syl22anc |
|
79 |
8
|
adantr |
|
80 |
59
|
adantr |
|
81 |
45
|
sseli |
|
82 |
81 64
|
sylan2 |
|
83 |
82
|
adantrr |
|
84 |
14
|
sselda |
|
85 |
84
|
adantrl |
|
86 |
83 85
|
ffvelrnd |
|
87 |
1
|
frlmsca |
|
88 |
87
|
3adant3 |
|
89 |
88
|
fveq2d |
|
90 |
89
|
adantr |
|
91 |
86 90
|
eleqtrd |
|
92 |
4 3
|
lspssid |
|
93 |
8 57 92
|
syl2anc |
|
94 |
93
|
adantr |
|
95 |
|
funfvima2 |
|
96 |
35 37 95
|
syl2anc |
|
97 |
96
|
imp |
|
98 |
97
|
adantrl |
|
99 |
94 98
|
sseldd |
|
100 |
|
eqid |
|
101 |
|
eqid |
|
102 |
100 48 101 9
|
lssvscl |
|
103 |
79 80 91 99 102
|
syl22anc |
|
104 |
103
|
anassrs |
|
105 |
104
|
adantlrr |
|
106 |
|
id |
|
107 |
106
|
adantrr |
|
108 |
107
|
adantr |
|
109 |
|
simplrr |
|
110 |
|
simpr |
|
111 |
109 110
|
eldifd |
|
112 |
|
oveq1 |
|
113 |
112
|
sseq1d |
|
114 |
113 6
|
elrab2 |
|
115 |
114
|
simprbi |
|
116 |
115
|
adantl |
|
117 |
5
|
fvexi |
|
118 |
117
|
a1i |
|
119 |
82 116 44 118
|
suppssr |
|
120 |
108 111 119
|
syl2anc |
|
121 |
88
|
fveq2d |
|
122 |
5 121
|
syl5eq |
|
123 |
122
|
ad2antrr |
|
124 |
120 123
|
eqtrd |
|
125 |
124
|
oveq1d |
|
126 |
8
|
ad2antrr |
|
127 |
12
|
ffvelrnda |
|
128 |
127
|
adantrl |
|
129 |
128
|
adantr |
|
130 |
|
eqid |
|
131 |
4 100 48 130 51
|
lmod0vs |
|
132 |
126 129 131
|
syl2anc |
|
133 |
125 132
|
eqtrd |
|
134 |
59
|
ad2antrr |
|
135 |
51 9
|
lss0cl |
|
136 |
126 134 135
|
syl2anc |
|
137 |
133 136
|
eqeltrd |
|
138 |
105 137
|
pm2.61dan |
|
139 |
78 138
|
eqeltrd |
|
140 |
139
|
expr |
|
141 |
140
|
ralrimiv |
|
142 |
|
ffnfv |
|
143 |
71 141 142
|
sylanbrc |
|
144 |
1 5 4
|
frlmbasfsupp |
|
145 |
144
|
fsuppimpd |
|
146 |
44 47 145
|
syl2anc |
|
147 |
|
dffn2 |
|
148 |
70 147
|
sylib |
|
149 |
65
|
adantr |
|
150 |
66
|
ad2antrr |
|
151 |
|
simpll2 |
|
152 |
|
eldifi |
|
153 |
152
|
adantl |
|
154 |
|
fnfvof |
|
155 |
149 150 151 153 154
|
syl22anc |
|
156 |
|
ssidd |
|
157 |
117
|
a1i |
|
158 |
64 156 68 157
|
suppssr |
|
159 |
122
|
ad2antrr |
|
160 |
158 159
|
eqtrd |
|
161 |
160
|
oveq1d |
|
162 |
8
|
ad2antrr |
|
163 |
12
|
adantr |
|
164 |
|
ffvelrn |
|
165 |
163 152 164
|
syl2an |
|
166 |
4 100 48 130 51
|
lmod0vs |
|
167 |
162 165 166
|
syl2anc |
|
168 |
155 161 167
|
3eqtrd |
|
169 |
148 168
|
suppss |
|
170 |
47 169
|
syldan |
|
171 |
146 170
|
ssfid |
|
172 |
|
simp2 |
|
173 |
1 18 4
|
frlmbasmap |
|
174 |
172 81 173
|
syl2an |
|
175 |
|
elmapfn |
|
176 |
174 175
|
syl |
|
177 |
12
|
adantr |
|
178 |
177
|
ffnd |
|
179 |
176 178 44 44
|
offun |
|
180 |
|
ovexd |
|
181 |
|
fvexd |
|
182 |
|
funisfsupp |
|
183 |
179 180 181 182
|
syl3anc |
|
184 |
171 183
|
mpbird |
|
185 |
51 54 44 62 143 184
|
gsumsubgcl |
|
186 |
50 185
|
eqeltrd |
|
187 |
42 186
|
eqelssd |
|