Step |
Hyp |
Ref |
Expression |
1 |
|
hoidmv1lelem3.a |
|
2 |
|
hoidmv1lelem3.b |
|
3 |
|
hoidmv1lelem3.l |
|
4 |
|
hoidmv1lelem3.c |
|
5 |
|
hoidmv1lelem3.d |
|
6 |
|
hoidmv1lelem3.x |
|
7 |
|
hoidmv1lelem3.r |
|
8 |
|
hoidmv1lelem3.u |
|
9 |
|
hoidmv1lelem3.s |
|
10 |
2 1
|
resubcld |
|
11 |
|
nnex |
|
12 |
11
|
a1i |
|
13 |
|
icossicc |
|
14 |
|
0xr |
|
15 |
14
|
a1i |
|
16 |
|
pnfxr |
|
17 |
16
|
a1i |
|
18 |
4
|
ffvelrnda |
|
19 |
5
|
ffvelrnda |
|
20 |
2
|
adantr |
|
21 |
19 20
|
ifcld |
|
22 |
|
volicore |
|
23 |
18 21 22
|
syl2anc |
|
24 |
23
|
rexrd |
|
25 |
21
|
rexrd |
|
26 |
|
icombl |
|
27 |
18 25 26
|
syl2anc |
|
28 |
|
volge0 |
|
29 |
27 28
|
syl |
|
30 |
23
|
ltpnfd |
|
31 |
15 17 24 29 30
|
elicod |
|
32 |
13 31
|
sseldi |
|
33 |
|
eqid |
|
34 |
32 33
|
fmptd |
|
35 |
12 34
|
sge0xrcl |
|
36 |
16
|
a1i |
|
37 |
7
|
rexrd |
|
38 |
|
nfv |
|
39 |
|
volf |
|
40 |
39
|
a1i |
|
41 |
19
|
rexrd |
|
42 |
|
icombl |
|
43 |
18 41 42
|
syl2anc |
|
44 |
40 43
|
ffvelrnd |
|
45 |
18
|
rexrd |
|
46 |
18
|
leidd |
|
47 |
|
min1 |
|
48 |
19 20 47
|
syl2anc |
|
49 |
|
icossico |
|
50 |
45 41 46 48 49
|
syl22anc |
|
51 |
|
volss |
|
52 |
27 43 50 51
|
syl3anc |
|
53 |
38 12 32 44 52
|
sge0lempt |
|
54 |
7
|
ltpnfd |
|
55 |
35 37 36 53 54
|
xrlelttrd |
|
56 |
35 36 55
|
xrltned |
|
57 |
56
|
neneqd |
|
58 |
12 34
|
sge0repnf |
|
59 |
57 58
|
mpbird |
|
60 |
2
|
rexrd |
|
61 |
1 2
|
iccssred |
|
62 |
|
ssrab2 |
|
63 |
8 62
|
eqsstri |
|
64 |
1 2 3 4 5 7 8 9
|
hoidmv1lelem1 |
|
65 |
64
|
simp1d |
|
66 |
63 65
|
sseldi |
|
67 |
61 66
|
sseldd |
|
68 |
67
|
rexrd |
|
69 |
|
simpl |
|
70 |
|
simpr |
|
71 |
69 67
|
syl |
|
72 |
69 2
|
syl |
|
73 |
71 72
|
ltnled |
|
74 |
70 73
|
mpbird |
|
75 |
6
|
adantr |
|
76 |
1
|
rexrd |
|
77 |
76
|
adantr |
|
78 |
60
|
adantr |
|
79 |
68
|
adantr |
|
80 |
63 61
|
sstrid |
|
81 |
65
|
ne0d |
|
82 |
64
|
simp3d |
|
83 |
64
|
simp2d |
|
84 |
|
suprub |
|
85 |
80 81 82 83 84
|
syl31anc |
|
86 |
85 9
|
breqtrrdi |
|
87 |
86
|
adantr |
|
88 |
|
simpr |
|
89 |
77 78 79 87 88
|
elicod |
|
90 |
75 89
|
sseldd |
|
91 |
|
eliun |
|
92 |
90 91
|
sylib |
|
93 |
1
|
adantr |
|
94 |
93
|
3ad2ant1 |
|
95 |
2
|
adantr |
|
96 |
95
|
3ad2ant1 |
|
97 |
4
|
adantr |
|
98 |
97
|
3ad2ant1 |
|
99 |
5
|
adantr |
|
100 |
99
|
3ad2ant1 |
|
101 |
|
fveq2 |
|
102 |
|
fveq2 |
|
103 |
101 102
|
oveq12d |
|
104 |
103
|
fveq2d |
|
105 |
104
|
cbvmptv |
|
106 |
105
|
fveq2i |
|
107 |
106 7
|
eqeltrid |
|
108 |
107
|
adantr |
|
109 |
108
|
3ad2ant1 |
|
110 |
102
|
breq1d |
|
111 |
110 102
|
ifbieq1d |
|
112 |
101 111
|
oveq12d |
|
113 |
112
|
fveq2d |
|
114 |
113
|
cbvmptv |
|
115 |
114
|
eqcomi |
|
116 |
115
|
fveq2i |
|
117 |
116
|
breq2i |
|
118 |
117
|
rabbii |
|
119 |
8 118
|
eqtri |
|
120 |
65
|
adantr |
|
121 |
120
|
3ad2ant1 |
|
122 |
87
|
3ad2ant1 |
|
123 |
88
|
3ad2ant1 |
|
124 |
|
simp2 |
|
125 |
|
simp3 |
|
126 |
|
eqid |
|
127 |
94 96 98 100 109 119 121 122 123 124 125 126
|
hoidmv1lelem2 |
|
128 |
127
|
3exp |
|
129 |
128
|
rexlimdv |
|
130 |
92 129
|
mpd |
|
131 |
69 74 130
|
syl2anc |
|
132 |
61
|
adantr |
|
133 |
63 132
|
sstrid |
|
134 |
81
|
adantr |
|
135 |
1 2
|
jca |
|
136 |
135
|
adantr |
|
137 |
63
|
a1i |
|
138 |
65
|
adantr |
|
139 |
|
iccsupr |
|
140 |
136 137 138 139
|
syl3anc |
|
141 |
140
|
simp3d |
|
142 |
|
simpr |
|
143 |
|
suprub |
|
144 |
133 134 141 142 143
|
syl31anc |
|
145 |
144 9
|
breqtrrdi |
|
146 |
145
|
ralrimiva |
|
147 |
63
|
sseli |
|
148 |
147
|
adantl |
|
149 |
132 148
|
sseldd |
|
150 |
67
|
adantr |
|
151 |
149 150
|
lenltd |
|
152 |
151
|
ralbidva |
|
153 |
146 152
|
mpbid |
|
154 |
|
ralnex |
|
155 |
153 154
|
sylib |
|
156 |
155
|
adantr |
|
157 |
131 156
|
condan |
|
158 |
|
iccleub |
|
159 |
76 60 66 158
|
syl3anc |
|
160 |
60 68 157 159
|
xrletrid |
|
161 |
160 65
|
eqeltrd |
|
162 |
161 8
|
eleqtrdi |
|
163 |
|
oveq1 |
|
164 |
|
breq2 |
|
165 |
|
id |
|
166 |
164 165
|
ifbieq2d |
|
167 |
166
|
oveq2d |
|
168 |
167
|
fveq2d |
|
169 |
168
|
mpteq2dv |
|
170 |
169
|
fveq2d |
|
171 |
163 170
|
breq12d |
|
172 |
171
|
elrab |
|
173 |
162 172
|
sylib |
|
174 |
173
|
simprd |
|
175 |
10 59 7 174 53
|
letrd |
|