Step |
Hyp |
Ref |
Expression |
1 |
|
vdw.r |
|
2 |
|
vdwlem9.k |
|
3 |
|
vdwlem9.s |
|
4 |
|
vdwlem10.m |
|
5 |
|
opeq1 |
|
6 |
5
|
breq1d |
|
7 |
6
|
orbi1d |
|
8 |
7
|
rexralbidv |
|
9 |
8
|
imbi2d |
|
10 |
|
opeq1 |
|
11 |
10
|
breq1d |
|
12 |
11
|
orbi1d |
|
13 |
12
|
rexralbidv |
|
14 |
13
|
imbi2d |
|
15 |
|
opeq1 |
|
16 |
15
|
breq1d |
|
17 |
16
|
orbi1d |
|
18 |
17
|
rexralbidv |
|
19 |
18
|
imbi2d |
|
20 |
|
opeq1 |
|
21 |
20
|
breq1d |
|
22 |
21
|
orbi1d |
|
23 |
22
|
rexralbidv |
|
24 |
23
|
imbi2d |
|
25 |
|
oveq1 |
|
26 |
25
|
raleqdv |
|
27 |
26
|
rexbidv |
|
28 |
27 3 1
|
rspcdva |
|
29 |
|
oveq2 |
|
30 |
29
|
oveq2d |
|
31 |
30
|
raleqdv |
|
32 |
31
|
cbvrexvw |
|
33 |
28 32
|
sylib |
|
34 |
|
breq2 |
|
35 |
34
|
cbvralvw |
|
36 |
|
2nn |
|
37 |
|
simpr |
|
38 |
|
nnmulcl |
|
39 |
36 37 38
|
sylancr |
|
40 |
1
|
adantr |
|
41 |
|
ovex |
|
42 |
|
elmapg |
|
43 |
40 41 42
|
sylancl |
|
44 |
43
|
biimpa |
|
45 |
|
simplr |
|
46 |
|
elfznn |
|
47 |
46
|
adantl |
|
48 |
47
|
nnred |
|
49 |
|
simpllr |
|
50 |
49
|
nnred |
|
51 |
|
elfzle2 |
|
52 |
51
|
adantl |
|
53 |
48 50 50 52
|
leadd1dd |
|
54 |
49
|
nncnd |
|
55 |
54
|
2timesd |
|
56 |
53 55
|
breqtrrd |
|
57 |
47 49
|
nnaddcld |
|
58 |
|
nnuz |
|
59 |
57 58
|
eleqtrdi |
|
60 |
39
|
ad2antrr |
|
61 |
60
|
nnzd |
|
62 |
|
elfz5 |
|
63 |
59 61 62
|
syl2anc |
|
64 |
56 63
|
mpbird |
|
65 |
45 64
|
ffvelrnd |
|
66 |
|
fvoveq1 |
|
67 |
66
|
cbvmptv |
|
68 |
65 67
|
fmptd |
|
69 |
|
ovex |
|
70 |
|
elmapg |
|
71 |
40 69 70
|
sylancl |
|
72 |
71
|
biimpar |
|
73 |
68 72
|
syldan |
|
74 |
|
breq2 |
|
75 |
74
|
rspcv |
|
76 |
73 75
|
syl |
|
77 |
|
2nn0 |
|
78 |
2
|
ad2antrr |
|
79 |
|
eluznn0 |
|
80 |
77 78 79
|
sylancr |
|
81 |
69 80 68
|
vdwmc |
|
82 |
40
|
ad2antrr |
|
83 |
78
|
adantr |
|
84 |
|
simpllr |
|
85 |
|
simplr |
|
86 |
|
vex |
|
87 |
|
simprll |
|
88 |
|
simprlr |
|
89 |
|
simprr |
|
90 |
82 83 84 85 86 87 88 89 67
|
vdwlem8 |
|
91 |
90
|
orcd |
|
92 |
91
|
expr |
|
93 |
92
|
rexlimdvva |
|
94 |
93
|
exlimdv |
|
95 |
81 94
|
sylbid |
|
96 |
76 95
|
syld |
|
97 |
44 96
|
syldan |
|
98 |
97
|
ralrimdva |
|
99 |
|
oveq2 |
|
100 |
99
|
oveq2d |
|
101 |
100
|
raleqdv |
|
102 |
101
|
rspcev |
|
103 |
39 98 102
|
syl6an |
|
104 |
35 103
|
syl5bi |
|
105 |
104
|
rexlimdva |
|
106 |
33 105
|
mpd |
|
107 |
|
breq2 |
|
108 |
|
breq2 |
|
109 |
107 108
|
orbi12d |
|
110 |
109
|
cbvralvw |
|
111 |
30
|
raleqdv |
|
112 |
110 111
|
syl5bb |
|
113 |
112
|
cbvrexvw |
|
114 |
|
oveq2 |
|
115 |
114
|
oveq2d |
|
116 |
115
|
raleqdv |
|
117 |
116
|
cbvrexvw |
|
118 |
|
oveq1 |
|
119 |
118
|
raleqdv |
|
120 |
119
|
rexbidv |
|
121 |
117 120
|
syl5bb |
|
122 |
3
|
ad2antrr |
|
123 |
1
|
ad2antrr |
|
124 |
|
fzfi |
|
125 |
|
mapfi |
|
126 |
123 124 125
|
sylancl |
|
127 |
121 122 126
|
rspcdva |
|
128 |
|
simprll |
|
129 |
|
simprrl |
|
130 |
|
nnmulcl |
|
131 |
36 130
|
mpan |
|
132 |
|
nnmulcl |
|
133 |
131 132
|
sylan2 |
|
134 |
128 129 133
|
syl2anc |
|
135 |
|
simp1l |
|
136 |
135 1
|
syl |
|
137 |
135 2
|
syl |
|
138 |
135 3
|
syl |
|
139 |
|
simp1r |
|
140 |
|
simp2ll |
|
141 |
|
simp2lr |
|
142 |
|
breq2 |
|
143 |
|
breq2 |
|
144 |
142 143
|
orbi12d |
|
145 |
144
|
cbvralvw |
|
146 |
141 145
|
sylib |
|
147 |
|
simp2rl |
|
148 |
|
simp2rr |
|
149 |
|
simp3 |
|
150 |
|
ovex |
|
151 |
|
elmapg |
|
152 |
136 150 151
|
sylancl |
|
153 |
149 152
|
mpbid |
|
154 |
|
fvoveq1 |
|
155 |
154
|
cbvmptv |
|
156 |
|
oveq1 |
|
157 |
156
|
oveq1d |
|
158 |
157
|
oveq2d |
|
159 |
158
|
oveq2d |
|
160 |
159
|
fveq2d |
|
161 |
160
|
mpteq2dv |
|
162 |
155 161
|
syl5eq |
|
163 |
162
|
cbvmptv |
|
164 |
136 137 138 139 140 146 147 148 153 163
|
vdwlem9 |
|
165 |
164
|
3expia |
|
166 |
165
|
ralrimiv |
|
167 |
|
oveq2 |
|
168 |
167
|
oveq2d |
|
169 |
168
|
raleqdv |
|
170 |
|
breq2 |
|
171 |
|
breq2 |
|
172 |
170 171
|
orbi12d |
|
173 |
172
|
cbvralvw |
|
174 |
169 173
|
bitrdi |
|
175 |
174
|
rspcev |
|
176 |
134 166 175
|
syl2anc |
|
177 |
176
|
anassrs |
|
178 |
127 177
|
rexlimddv |
|
179 |
178
|
rexlimdvaa |
|
180 |
113 179
|
syl5bi |
|
181 |
180
|
expcom |
|
182 |
181
|
a2d |
|
183 |
9 14 19 24 106 182
|
nnind |
|
184 |
4 183
|
mpcom |
|