Step |
Hyp |
Ref |
Expression |
1 |
|
tsmsres.b |
|
2 |
|
tsmsres.z |
|
3 |
|
tsmsres.1 |
|
4 |
|
tsmsres.2 |
|
5 |
|
tsmsres.a |
|
6 |
|
tsmsres.f |
|
7 |
|
tsmsres.s |
|
8 |
|
inss1 |
|
9 |
8
|
sspwi |
|
10 |
|
ssrin |
|
11 |
9 10
|
ax-mp |
|
12 |
|
simpr |
|
13 |
11 12
|
sseldi |
|
14 |
|
elfpw |
|
15 |
14
|
simplbi |
|
16 |
15
|
adantl |
|
17 |
16
|
ssrind |
|
18 |
|
elinel2 |
|
19 |
18
|
adantl |
|
20 |
|
inss1 |
|
21 |
|
ssfi |
|
22 |
19 20 21
|
sylancl |
|
23 |
|
elfpw |
|
24 |
17 22 23
|
sylanbrc |
|
25 |
|
sseq2 |
|
26 |
|
ssin |
|
27 |
25 26
|
bitr4di |
|
28 |
|
reseq2 |
|
29 |
|
inss2 |
|
30 |
|
resabs1 |
|
31 |
29 30
|
ax-mp |
|
32 |
28 31
|
eqtrdi |
|
33 |
32
|
oveq2d |
|
34 |
33
|
eleq1d |
|
35 |
27 34
|
imbi12d |
|
36 |
35
|
rspcv |
|
37 |
24 36
|
syl |
|
38 |
|
elfpw |
|
39 |
38
|
simplbi |
|
40 |
39
|
ad2antlr |
|
41 |
|
inss2 |
|
42 |
40 41
|
sstrdi |
|
43 |
42
|
biantrud |
|
44 |
|
resres |
|
45 |
44
|
oveq2i |
|
46 |
3
|
ad2antrr |
|
47 |
6
|
ad2antrr |
|
48 |
47 16
|
fssresd |
|
49 |
|
fex |
|
50 |
6 5 49
|
syl2anc |
|
51 |
50
|
ad2antrr |
|
52 |
2
|
fvexi |
|
53 |
|
ressuppss |
|
54 |
51 52 53
|
sylancl |
|
55 |
7
|
ad2antrr |
|
56 |
54 55
|
sstrd |
|
57 |
52
|
a1i |
|
58 |
48 19 57
|
fdmfifsupp |
|
59 |
1 2 46 19 48 56 58
|
gsumres |
|
60 |
45 59
|
syl5reqr |
|
61 |
60
|
eleq1d |
|
62 |
43 61
|
imbi12d |
|
63 |
37 62
|
sylibrd |
|
64 |
63
|
ralrimdva |
|
65 |
|
sseq1 |
|
66 |
65
|
rspceaimv |
|
67 |
13 64 66
|
syl6an |
|
68 |
67
|
rexlimdva |
|
69 |
|
elfpw |
|
70 |
69
|
simplbi |
|
71 |
70
|
adantl |
|
72 |
71
|
ssrind |
|
73 |
|
elinel2 |
|
74 |
73
|
adantl |
|
75 |
|
inss1 |
|
76 |
|
ssfi |
|
77 |
74 75 76
|
sylancl |
|
78 |
|
elfpw |
|
79 |
72 77 78
|
sylanbrc |
|
80 |
70
|
ad2antlr |
|
81 |
|
elfpw |
|
82 |
81
|
simplbi |
|
83 |
82
|
adantl |
|
84 |
83 8
|
sstrdi |
|
85 |
80 84
|
unssd |
|
86 |
|
elinel2 |
|
87 |
|
unfi |
|
88 |
74 86 87
|
syl2an |
|
89 |
|
elfpw |
|
90 |
85 88 89
|
sylanbrc |
|
91 |
|
ssun1 |
|
92 |
|
id |
|
93 |
91 92
|
sseqtrrid |
|
94 |
|
pm5.5 |
|
95 |
93 94
|
syl |
|
96 |
|
reseq2 |
|
97 |
96
|
oveq2d |
|
98 |
97
|
eleq1d |
|
99 |
95 98
|
bitrd |
|
100 |
99
|
rspcv |
|
101 |
90 100
|
syl |
|
102 |
3
|
ad2antrr |
|
103 |
88
|
adantrr |
|
104 |
6
|
ad2antrr |
|
105 |
85
|
adantrr |
|
106 |
104 105
|
fssresd |
|
107 |
50 52
|
jctir |
|
108 |
107
|
ad2antrr |
|
109 |
|
ressuppss |
|
110 |
108 109
|
syl |
|
111 |
7
|
ad2antrr |
|
112 |
110 111
|
sstrd |
|
113 |
52
|
a1i |
|
114 |
106 103 113
|
fdmfifsupp |
|
115 |
1 2 102 103 106 112 114
|
gsumres |
|
116 |
|
resres |
|
117 |
|
indir |
|
118 |
83 41
|
sstrdi |
|
119 |
118
|
adantrr |
|
120 |
|
df-ss |
|
121 |
119 120
|
sylib |
|
122 |
121
|
uneq2d |
|
123 |
|
simprr |
|
124 |
|
ssequn1 |
|
125 |
123 124
|
sylib |
|
126 |
122 125
|
eqtrd |
|
127 |
117 126
|
syl5eq |
|
128 |
127
|
reseq2d |
|
129 |
116 128
|
syl5eq |
|
130 |
119
|
resabs1d |
|
131 |
129 130
|
eqtr4d |
|
132 |
131
|
oveq2d |
|
133 |
115 132
|
eqtr3d |
|
134 |
133
|
eleq1d |
|
135 |
134
|
biimpd |
|
136 |
135
|
expr |
|
137 |
136
|
com23 |
|
138 |
101 137
|
syld |
|
139 |
138
|
ralrimdva |
|
140 |
|
sseq1 |
|
141 |
140
|
rspceaimv |
|
142 |
79 139 141
|
syl6an |
|
143 |
142
|
rexlimdva |
|
144 |
68 143
|
impbid |
|
145 |
144
|
imbi2d |
|
146 |
145
|
ralbidv |
|
147 |
146
|
anbi2d |
|
148 |
|
eqid |
|
149 |
|
eqid |
|
150 |
|
inex1g |
|
151 |
5 150
|
syl |
|
152 |
|
fssres |
|
153 |
6 8 152
|
sylancl |
|
154 |
|
resres |
|
155 |
|
ffn |
|
156 |
|
fnresdm |
|
157 |
6 155 156
|
3syl |
|
158 |
157
|
reseq1d |
|
159 |
154 158
|
syl5eqr |
|
160 |
159
|
feq1d |
|
161 |
153 160
|
mpbid |
|
162 |
1 148 149 3 4 151 161
|
eltsms |
|
163 |
|
eqid |
|
164 |
1 148 163 3 4 5 6
|
eltsms |
|
165 |
147 162 164
|
3bitr4d |
|
166 |
165
|
eqrdv |
|