Step |
Hyp |
Ref |
Expression |
1 |
|
subgdprd.1 |
|
2 |
|
reldmdprd |
|
3 |
2
|
brrelex2i |
|
4 |
3
|
a1i |
|
5 |
2
|
brrelex2i |
|
6 |
5
|
adantr |
|
7 |
6
|
a1i |
|
8 |
|
ffvelrn |
|
9 |
8
|
ad2ant2lr |
|
10 |
|
eqid |
|
11 |
10
|
subgss |
|
12 |
9 11
|
syl |
|
13 |
1
|
subgbas |
|
14 |
13
|
ad2antrr |
|
15 |
12 14
|
sseqtrrd |
|
16 |
15
|
biantrud |
|
17 |
|
simpll |
|
18 |
|
simplr |
|
19 |
|
eldifi |
|
20 |
19
|
ad2antll |
|
21 |
18 20
|
ffvelrnd |
|
22 |
10
|
subgss |
|
23 |
21 22
|
syl |
|
24 |
23 14
|
sseqtrrd |
|
25 |
|
eqid |
|
26 |
|
eqid |
|
27 |
1 25 26
|
resscntz |
|
28 |
17 24 27
|
syl2anc |
|
29 |
28
|
sseq2d |
|
30 |
|
ssin |
|
31 |
29 30
|
bitr4di |
|
32 |
16 31
|
bitr4d |
|
33 |
32
|
anassrs |
|
34 |
33
|
ralbidva |
|
35 |
|
subgrcl |
|
36 |
35
|
ad2antrr |
|
37 |
|
eqid |
|
38 |
37
|
subgacs |
|
39 |
|
acsmre |
|
40 |
36 38 39
|
3syl |
|
41 |
1
|
subggrp |
|
42 |
41
|
ad2antrr |
|
43 |
10
|
subgacs |
|
44 |
|
acsmre |
|
45 |
42 43 44
|
3syl |
|
46 |
|
eqid |
|
47 |
|
imassrn |
|
48 |
|
frn |
|
49 |
48
|
ad2antlr |
|
50 |
47 49
|
sstrid |
|
51 |
|
mresspw |
|
52 |
45 51
|
syl |
|
53 |
50 52
|
sstrd |
|
54 |
|
sspwuni |
|
55 |
53 54
|
sylib |
|
56 |
45 46 55
|
mrcssidd |
|
57 |
46
|
mrccl |
|
58 |
45 55 57
|
syl2anc |
|
59 |
1
|
subsubg |
|
60 |
59
|
ad2antrr |
|
61 |
58 60
|
mpbid |
|
62 |
61
|
simpld |
|
63 |
|
eqid |
|
64 |
63
|
mrcsscl |
|
65 |
40 56 62 64
|
syl3anc |
|
66 |
13
|
ad2antrr |
|
67 |
55 66
|
sseqtrrd |
|
68 |
37
|
subgss |
|
69 |
68
|
ad2antrr |
|
70 |
67 69
|
sstrd |
|
71 |
40 63 70
|
mrcssidd |
|
72 |
63
|
mrccl |
|
73 |
40 70 72
|
syl2anc |
|
74 |
|
simpll |
|
75 |
63
|
mrcsscl |
|
76 |
40 67 74 75
|
syl3anc |
|
77 |
1
|
subsubg |
|
78 |
77
|
ad2antrr |
|
79 |
73 76 78
|
mpbir2and |
|
80 |
46
|
mrcsscl |
|
81 |
45 71 79 80
|
syl3anc |
|
82 |
65 81
|
eqssd |
|
83 |
82
|
ineq2d |
|
84 |
|
eqid |
|
85 |
1 84
|
subg0 |
|
86 |
85
|
ad2antrr |
|
87 |
86
|
sneqd |
|
88 |
83 87
|
eqeq12d |
|
89 |
34 88
|
anbi12d |
|
90 |
89
|
ralbidva |
|
91 |
90
|
pm5.32da |
|
92 |
1
|
subsubg |
|
93 |
|
elin |
|
94 |
|
velpw |
|
95 |
94
|
anbi2i |
|
96 |
93 95
|
bitri |
|
97 |
92 96
|
bitr4di |
|
98 |
97
|
eqrdv |
|
99 |
98
|
sseq2d |
|
100 |
|
ssin |
|
101 |
99 100
|
bitr4di |
|
102 |
101
|
anbi2d |
|
103 |
|
df-f |
|
104 |
|
df-f |
|
105 |
104
|
anbi1i |
|
106 |
|
anass |
|
107 |
105 106
|
bitri |
|
108 |
102 103 107
|
3bitr4g |
|
109 |
108
|
anbi1d |
|
110 |
91 109
|
bitr3d |
|
111 |
110
|
adantr |
|
112 |
|
dmexg |
|
113 |
112
|
adantl |
|
114 |
|
eqidd |
|
115 |
41
|
adantr |
|
116 |
|
eqid |
|
117 |
26 116 46
|
dmdprd |
|
118 |
|
3anass |
|
119 |
117 118
|
bitrdi |
|
120 |
119
|
baibd |
|
121 |
113 114 115 120
|
syl21anc |
|
122 |
35
|
adantr |
|
123 |
25 84 63
|
dmdprd |
|
124 |
|
3anass |
|
125 |
123 124
|
bitrdi |
|
126 |
125
|
baibd |
|
127 |
113 114 122 126
|
syl21anc |
|
128 |
127
|
anbi1d |
|
129 |
|
an32 |
|
130 |
128 129
|
bitrdi |
|
131 |
111 121 130
|
3bitr4d |
|
132 |
131
|
ex |
|
133 |
4 7 132
|
pm5.21ndd |
|