Step |
Hyp |
Ref |
Expression |
1 |
|
breq2 |
|
2 |
|
simp3 |
|
3 |
|
simp1l |
|
4 |
1 2 3
|
rspcdva |
|
5 |
|
simpl21 |
|
6 |
|
simpl1l |
|
7 |
5 6
|
sseldd |
|
8 |
|
nodmon |
|
9 |
7 8
|
syl |
|
10 |
|
onelon |
|
11 |
9 10
|
sylan |
|
12 |
|
simpr |
|
13 |
|
simplr |
|
14 |
9
|
adantr |
|
15 |
14
|
adantr |
|
16 |
|
ontr1 |
|
17 |
15 16
|
syl |
|
18 |
12 13 17
|
mp2and |
|
19 |
18
|
fvresd |
|
20 |
|
onelon |
|
21 |
11 20
|
sylan |
|
22 |
|
fveq2 |
|
23 |
|
fveq2 |
|
24 |
22 23
|
neeq12d |
|
25 |
24
|
onnminsb |
|
26 |
21 12 25
|
sylc |
|
27 |
|
df-ne |
|
28 |
27
|
con2bii |
|
29 |
26 28
|
sylibr |
|
30 |
19 29
|
eqtr4d |
|
31 |
30
|
ralrimiva |
|
32 |
|
simpr |
|
33 |
32
|
fvresd |
|
34 |
|
simplr |
|
35 |
|
simpl23 |
|
36 |
7
|
adantr |
|
37 |
|
sltval2 |
|
38 |
35 36 37
|
syl2an2r |
|
39 |
34 38
|
mpbid |
|
40 |
|
necom |
|
41 |
40
|
rabbii |
|
42 |
41
|
inteqi |
|
43 |
42
|
fveq2i |
|
44 |
42
|
fveq2i |
|
45 |
39 43 44
|
3brtr4g |
|
46 |
33 45
|
eqbrtrd |
|
47 |
|
raleq |
|
48 |
|
fveq2 |
|
49 |
|
fveq2 |
|
50 |
48 49
|
breq12d |
|
51 |
47 50
|
anbi12d |
|
52 |
51
|
rspcev |
|
53 |
11 31 46 52
|
syl12anc |
|
54 |
|
noreson |
|
55 |
35 9 54
|
syl2anc |
|
56 |
|
sltval |
|
57 |
55 36 56
|
syl2an2r |
|
58 |
53 57
|
mpbird |
|
59 |
|
sssucid |
|
60 |
|
resabs1 |
|
61 |
59 60
|
mp1i |
|
62 |
|
resundir |
|
63 |
|
nofun |
|
64 |
7 63
|
syl |
|
65 |
|
funrel |
|
66 |
64 65
|
syl |
|
67 |
66
|
adantr |
|
68 |
|
resdm |
|
69 |
67 68
|
syl |
|
70 |
|
nodmord |
|
71 |
7 70
|
syl |
|
72 |
71
|
adantr |
|
73 |
|
ordirr |
|
74 |
72 73
|
syl |
|
75 |
|
1oex |
|
76 |
75
|
snres0 |
|
77 |
74 76
|
sylibr |
|
78 |
69 77
|
uneq12d |
|
79 |
|
un0 |
|
80 |
78 79
|
eqtrdi |
|
81 |
62 80
|
syl5eq |
|
82 |
58 61 81
|
3brtr4d |
|
83 |
|
sucelon |
|
84 |
9 83
|
sylib |
|
85 |
|
noreson |
|
86 |
35 84 85
|
syl2anc |
|
87 |
86
|
adantr |
|
88 |
75
|
prid1 |
|
89 |
88
|
noextend |
|
90 |
7 89
|
syl |
|
91 |
90
|
adantr |
|
92 |
|
sltres |
|
93 |
87 91 14 92
|
syl3anc |
|
94 |
82 93
|
mpd |
|
95 |
|
sltso |
|
96 |
|
soasym |
|
97 |
95 96
|
mpan |
|
98 |
86 91 97
|
syl2an2r |
|
99 |
94 98
|
mpd |
|
100 |
|
sonr |
|
101 |
95 90 100
|
sylancr |
|
102 |
101
|
adantr |
|
103 |
|
df-suc |
|
104 |
103
|
reseq2i |
|
105 |
|
resundi |
|
106 |
104 105
|
eqtri |
|
107 |
|
dmres |
|
108 |
42
|
eqeq1i |
|
109 |
108
|
biimpi |
|
110 |
109
|
adantl |
|
111 |
35
|
adantr |
|
112 |
7
|
adantr |
|
113 |
|
simp23 |
|
114 |
|
sonr |
|
115 |
95 113 114
|
sylancr |
|
116 |
|
breq2 |
|
117 |
116
|
notbid |
|
118 |
115 117
|
syl5ibrcom |
|
119 |
118
|
necon2ad |
|
120 |
119
|
imp |
|
121 |
120
|
necomd |
|
122 |
121
|
adantr |
|
123 |
|
nosepssdm |
|
124 |
111 112 122 123
|
syl3anc |
|
125 |
110 124
|
eqsstrrd |
|
126 |
|
df-ss |
|
127 |
125 126
|
sylib |
|
128 |
107 127
|
syl5eq |
|
129 |
128
|
eleq2d |
|
130 |
|
simpr |
|
131 |
130
|
fvresd |
|
132 |
112 8
|
syl |
|
133 |
|
onelon |
|
134 |
132 133
|
sylan |
|
135 |
|
simpr |
|
136 |
135
|
eleq2d |
|
137 |
136
|
biimpar |
|
138 |
134 137 25
|
sylc |
|
139 |
|
nesym |
|
140 |
139
|
con2bii |
|
141 |
138 140
|
sylibr |
|
142 |
131 141
|
eqtrd |
|
143 |
142
|
ex |
|
144 |
129 143
|
sylbid |
|
145 |
144
|
ralrimiv |
|
146 |
|
nofun |
|
147 |
111 146
|
syl |
|
148 |
147
|
funresd |
|
149 |
64
|
adantr |
|
150 |
|
eqfunfv |
|
151 |
148 149 150
|
syl2anc |
|
152 |
128 145 151
|
mpbir2and |
|
153 |
35 146
|
syl |
|
154 |
153
|
funfnd |
|
155 |
112 70
|
syl |
|
156 |
155 73
|
syl |
|
157 |
|
ndmfv |
|
158 |
|
2on0 |
|
159 |
158
|
necomi |
|
160 |
|
neeq1 |
|
161 |
159 160
|
mpbiri |
|
162 |
161
|
neneqd |
|
163 |
157 162
|
syl |
|
164 |
156 163
|
syl |
|
165 |
164
|
intnand |
|
166 |
|
simpr |
|
167 |
35 7 37
|
syl2anc |
|
168 |
166 167
|
mpbid |
|
169 |
168
|
adantr |
|
170 |
110
|
fveq2d |
|
171 |
110
|
fveq2d |
|
172 |
169 170 171
|
3brtr3d |
|
173 |
|
fvex |
|
174 |
|
fvex |
|
175 |
173 174
|
brtp |
|
176 |
172 175
|
sylib |
|
177 |
|
3orel3 |
|
178 |
165 176 177
|
sylc |
|
179 |
|
andi |
|
180 |
178 179
|
sylibr |
|
181 |
180
|
simpld |
|
182 |
|
ndmfv |
|
183 |
|
1n0 |
|
184 |
183
|
necomi |
|
185 |
|
neeq1 |
|
186 |
184 185
|
mpbiri |
|
187 |
186
|
neneqd |
|
188 |
182 187
|
syl |
|
189 |
188
|
con4i |
|
190 |
181 189
|
syl |
|
191 |
|
fnressn |
|
192 |
154 190 191
|
syl2an2r |
|
193 |
181
|
opeq2d |
|
194 |
193
|
sneqd |
|
195 |
192 194
|
eqtrd |
|
196 |
152 195
|
uneq12d |
|
197 |
106 196
|
syl5eq |
|
198 |
197
|
breq2d |
|
199 |
102 198
|
mtbird |
|
200 |
|
nosepssdm |
|
201 |
7 35 120 200
|
syl3anc |
|
202 |
|
nosepon |
|
203 |
7 35 120 202
|
syl3anc |
|
204 |
|
onsseleq |
|
205 |
203 9 204
|
syl2anc |
|
206 |
201 205
|
mpbid |
|
207 |
99 199 206
|
mpjaodan |
|
208 |
4 207
|
mpdan |
|