Step |
Hyp |
Ref |
Expression |
1 |
|
mplsubglem.s |
|
2 |
|
mplsubglem.b |
|
3 |
|
mplsubglem.z |
|
4 |
|
mplsubglem.d |
|
5 |
|
mplsubglem.i |
|
6 |
|
mplsubglem.0 |
|
7 |
|
mplsubglem.a |
|
8 |
|
mplsubglem.y |
|
9 |
|
mplsubglem.u |
|
10 |
|
mplsubglem.r |
|
11 |
|
ssrab2 |
|
12 |
9 11
|
eqsstrdi |
|
13 |
1 5 10 4 3 2
|
psr0cl |
|
14 |
|
eqid |
|
15 |
14 3
|
grpidcl |
|
16 |
|
fconst6g |
|
17 |
10 15 16
|
3syl |
|
18 |
|
eldifi |
|
19 |
3
|
fvexi |
|
20 |
19
|
fvconst2 |
|
21 |
18 20
|
syl |
|
22 |
21
|
adantl |
|
23 |
17 22
|
suppss |
|
24 |
|
ss0 |
|
25 |
23 24
|
syl |
|
26 |
25 6
|
eqeltrd |
|
27 |
9
|
eleq2d |
|
28 |
|
oveq1 |
|
29 |
28
|
eleq1d |
|
30 |
29
|
elrab |
|
31 |
27 30
|
bitrdi |
|
32 |
13 26 31
|
mpbir2and |
|
33 |
32
|
ne0d |
|
34 |
|
eqid |
|
35 |
10
|
grpmgmd |
|
36 |
35
|
ad2antrr |
|
37 |
9
|
eleq2d |
|
38 |
|
oveq1 |
|
39 |
38
|
eleq1d |
|
40 |
39
|
elrab |
|
41 |
37 40
|
bitrdi |
|
42 |
41
|
biimpa |
|
43 |
42
|
simpld |
|
44 |
43
|
adantr |
|
45 |
9
|
adantr |
|
46 |
45
|
eleq2d |
|
47 |
|
oveq1 |
|
48 |
47
|
eleq1d |
|
49 |
48
|
elrab |
|
50 |
46 49
|
bitrdi |
|
51 |
50
|
biimpa |
|
52 |
51
|
simpld |
|
53 |
1 2 34 36 44 52
|
psraddcl |
|
54 |
|
ovexd |
|
55 |
|
sseq2 |
|
56 |
55
|
imbi1d |
|
57 |
56
|
albidv |
|
58 |
8
|
expr |
|
59 |
58
|
alrimiv |
|
60 |
59
|
ralrimiva |
|
61 |
60
|
ad2antrr |
|
62 |
42
|
simprd |
|
63 |
62
|
adantr |
|
64 |
51
|
simprd |
|
65 |
7
|
ralrimivva |
|
66 |
65
|
ad2antrr |
|
67 |
|
uneq1 |
|
68 |
67
|
eleq1d |
|
69 |
|
uneq2 |
|
70 |
69
|
eleq1d |
|
71 |
68 70
|
rspc2va |
|
72 |
63 64 66 71
|
syl21anc |
|
73 |
57 61 72
|
rspcdva |
|
74 |
1 14 4 2 53
|
psrelbas |
|
75 |
|
eqid |
|
76 |
1 2 75 34 44 52
|
psradd |
|
77 |
76
|
fveq1d |
|
78 |
77
|
adantr |
|
79 |
|
eldifi |
|
80 |
1 14 4 2 43
|
psrelbas |
|
81 |
80
|
adantr |
|
82 |
81
|
ffnd |
|
83 |
1 14 4 2 52
|
psrelbas |
|
84 |
83
|
ffnd |
|
85 |
|
ovex |
|
86 |
4 85
|
rabex2 |
|
87 |
86
|
a1i |
|
88 |
|
inidm |
|
89 |
|
eqidd |
|
90 |
|
eqidd |
|
91 |
82 84 87 87 88 89 90
|
ofval |
|
92 |
79 91
|
sylan2 |
|
93 |
|
ssun1 |
|
94 |
|
sscon |
|
95 |
93 94
|
ax-mp |
|
96 |
95
|
sseli |
|
97 |
|
ssidd |
|
98 |
86
|
a1i |
|
99 |
19
|
a1i |
|
100 |
80 97 98 99
|
suppssr |
|
101 |
100
|
adantlr |
|
102 |
96 101
|
sylan2 |
|
103 |
|
ssun2 |
|
104 |
|
sscon |
|
105 |
103 104
|
ax-mp |
|
106 |
105
|
sseli |
|
107 |
|
ssidd |
|
108 |
19
|
a1i |
|
109 |
83 107 87 108
|
suppssr |
|
110 |
106 109
|
sylan2 |
|
111 |
102 110
|
oveq12d |
|
112 |
10
|
ad2antrr |
|
113 |
14 75 3
|
grplid |
|
114 |
112 15 113
|
syl2anc2 |
|
115 |
114
|
adantr |
|
116 |
111 115
|
eqtrd |
|
117 |
78 92 116
|
3eqtrd |
|
118 |
74 117
|
suppss |
|
119 |
|
sseq1 |
|
120 |
|
eleq1 |
|
121 |
119 120
|
imbi12d |
|
122 |
121
|
spcgv |
|
123 |
54 73 118 122
|
syl3c |
|
124 |
9
|
ad2antrr |
|
125 |
124
|
eleq2d |
|
126 |
|
oveq1 |
|
127 |
126
|
eleq1d |
|
128 |
127
|
elrab |
|
129 |
125 128
|
bitrdi |
|
130 |
53 123 129
|
mpbir2and |
|
131 |
130
|
ralrimiva |
|
132 |
1 5 10
|
psrgrp |
|
133 |
|
eqid |
|
134 |
2 133
|
grpinvcl |
|
135 |
132 43 134
|
syl2an2r |
|
136 |
|
ovexd |
|
137 |
|
sseq2 |
|
138 |
137
|
imbi1d |
|
139 |
138
|
albidv |
|
140 |
60
|
adantr |
|
141 |
139 140 62
|
rspcdva |
|
142 |
5
|
adantr |
|
143 |
10
|
adantr |
|
144 |
|
eqid |
|
145 |
1 142 143 4 144 2 133 43
|
psrneg |
|
146 |
145
|
oveq1d |
|
147 |
14 144
|
grpinvfn |
|
148 |
147
|
a1i |
|
149 |
3 144
|
grpinvid |
|
150 |
143 149
|
syl |
|
151 |
148 80 98 99 150
|
suppcoss |
|
152 |
146 151
|
eqsstrd |
|
153 |
|
sseq1 |
|
154 |
|
eleq1 |
|
155 |
153 154
|
imbi12d |
|
156 |
155
|
spcgv |
|
157 |
136 141 152 156
|
syl3c |
|
158 |
45
|
eleq2d |
|
159 |
|
oveq1 |
|
160 |
159
|
eleq1d |
|
161 |
160
|
elrab |
|
162 |
158 161
|
bitrdi |
|
163 |
135 157 162
|
mpbir2and |
|
164 |
131 163
|
jca |
|
165 |
164
|
ralrimiva |
|
166 |
2 34 133
|
issubg2 |
|
167 |
132 166
|
syl |
|
168 |
12 33 165 167
|
mpbir3and |
|