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