Step |
Hyp |
Ref |
Expression |
1 |
|
mrsubco.s |
|
2 |
|
mrsubvrs.v |
|
3 |
|
mrsubvrs.r |
|
4 |
|
n0i |
|
5 |
1
|
rnfvprc |
|
6 |
4 5
|
nsyl2 |
|
7 |
|
eqid |
|
8 |
7 2 3
|
mrexval |
|
9 |
6 8
|
syl |
|
10 |
9
|
eleq2d |
|
11 |
|
fveq2 |
|
12 |
11
|
rneqd |
|
13 |
12
|
ineq1d |
|
14 |
|
rneq |
|
15 |
|
rn0 |
|
16 |
14 15
|
eqtrdi |
|
17 |
16
|
ineq1d |
|
18 |
|
0in |
|
19 |
17 18
|
eqtrdi |
|
20 |
19
|
iuneq1d |
|
21 |
|
0iun |
|
22 |
20 21
|
eqtrdi |
|
23 |
13 22
|
eqeq12d |
|
24 |
23
|
imbi2d |
|
25 |
|
fveq2 |
|
26 |
25
|
rneqd |
|
27 |
26
|
ineq1d |
|
28 |
|
rneq |
|
29 |
28
|
ineq1d |
|
30 |
29
|
iuneq1d |
|
31 |
27 30
|
eqeq12d |
|
32 |
31
|
imbi2d |
|
33 |
|
fveq2 |
|
34 |
33
|
rneqd |
|
35 |
34
|
ineq1d |
|
36 |
|
rneq |
|
37 |
36
|
ineq1d |
|
38 |
37
|
iuneq1d |
|
39 |
35 38
|
eqeq12d |
|
40 |
39
|
imbi2d |
|
41 |
|
fveq2 |
|
42 |
41
|
rneqd |
|
43 |
42
|
ineq1d |
|
44 |
|
rneq |
|
45 |
44
|
ineq1d |
|
46 |
45
|
iuneq1d |
|
47 |
43 46
|
eqeq12d |
|
48 |
47
|
imbi2d |
|
49 |
1
|
mrsub0 |
|
50 |
49
|
rneqd |
|
51 |
50 15
|
eqtrdi |
|
52 |
51
|
ineq1d |
|
53 |
52 18
|
eqtrdi |
|
54 |
|
uneq1 |
|
55 |
|
simpl |
|
56 |
|
simprl |
|
57 |
9
|
adantr |
|
58 |
56 57
|
eleqtrrd |
|
59 |
|
simprr |
|
60 |
59
|
s1cld |
|
61 |
60 57
|
eleqtrrd |
|
62 |
1 3
|
mrsubccat |
|
63 |
55 58 61 62
|
syl3anc |
|
64 |
63
|
rneqd |
|
65 |
1 3
|
mrsubf |
|
66 |
65
|
adantr |
|
67 |
66 58
|
ffvelrnd |
|
68 |
67 57
|
eleqtrd |
|
69 |
66 61
|
ffvelrnd |
|
70 |
69 57
|
eleqtrd |
|
71 |
|
ccatrn |
|
72 |
68 70 71
|
syl2anc |
|
73 |
64 72
|
eqtrd |
|
74 |
73
|
ineq1d |
|
75 |
|
indir |
|
76 |
74 75
|
eqtrdi |
|
77 |
|
ccatrn |
|
78 |
56 60 77
|
syl2anc |
|
79 |
|
s1rn |
|
80 |
79
|
ad2antll |
|
81 |
80
|
uneq2d |
|
82 |
78 81
|
eqtrd |
|
83 |
82
|
ineq1d |
|
84 |
|
indir |
|
85 |
83 84
|
eqtrdi |
|
86 |
85
|
iuneq1d |
|
87 |
|
iunxun |
|
88 |
86 87
|
eqtrdi |
|
89 |
|
simpr |
|
90 |
89
|
snssd |
|
91 |
|
df-ss |
|
92 |
90 91
|
sylib |
|
93 |
92
|
iuneq1d |
|
94 |
|
vex |
|
95 |
|
s1eq |
|
96 |
95
|
fveq2d |
|
97 |
96
|
rneqd |
|
98 |
97
|
ineq1d |
|
99 |
94 98
|
iunxsn |
|
100 |
93 99
|
eqtrdi |
|
101 |
|
incom |
|
102 |
|
simpr |
|
103 |
|
disjsn |
|
104 |
102 103
|
sylibr |
|
105 |
101 104
|
syl5eq |
|
106 |
105
|
iuneq1d |
|
107 |
55
|
adantr |
|
108 |
|
eldif |
|
109 |
108
|
biimpri |
|
110 |
59 109
|
sylan |
|
111 |
|
difun2 |
|
112 |
110 111
|
eleqtrdi |
|
113 |
1 3 2 7
|
mrsubcn |
|
114 |
107 112 113
|
syl2anc |
|
115 |
114
|
rneqd |
|
116 |
80
|
adantr |
|
117 |
115 116
|
eqtrd |
|
118 |
117
|
ineq1d |
|
119 |
118 105
|
eqtrd |
|
120 |
21 106 119
|
3eqtr4a |
|
121 |
100 120
|
pm2.61dan |
|
122 |
121
|
uneq2d |
|
123 |
88 122
|
eqtrd |
|
124 |
76 123
|
eqeq12d |
|
125 |
54 124
|
syl5ibr |
|
126 |
125
|
expcom |
|
127 |
126
|
a2d |
|
128 |
24 32 40 48 53 127
|
wrdind |
|
129 |
128
|
com12 |
|
130 |
10 129
|
sylbid |
|
131 |
130
|
imp |
|