Step |
Hyp |
Ref |
Expression |
1 |
|
peano2re |
|
2 |
|
ltp1 |
|
3 |
|
breq2 |
|
4 |
3
|
rspcev |
|
5 |
1 2 4
|
syl2anc |
|
6 |
5
|
rgen |
|
7 |
|
ltnle |
|
8 |
7
|
rexbidva |
|
9 |
|
rexnal |
|
10 |
8 9
|
bitrdi |
|
11 |
10
|
ralbiia |
|
12 |
|
ralnex |
|
13 |
11 12
|
bitri |
|
14 |
6 13
|
mpbi |
|
15 |
|
raleq |
|
16 |
15
|
rexbidv |
|
17 |
14 16
|
mtbiri |
|
18 |
|
ssrab2 |
|
19 |
|
ssrab2 |
|
20 |
|
zre |
|
21 |
|
2re |
|
22 |
|
reexpcl |
|
23 |
21 22
|
mpan |
|
24 |
|
nn0z |
|
25 |
|
2cn |
|
26 |
|
2ne0 |
|
27 |
|
expne0i |
|
28 |
25 26 27
|
mp3an12 |
|
29 |
24 28
|
syl |
|
30 |
23 29
|
jca |
|
31 |
|
redivcl |
|
32 |
|
peano2re |
|
33 |
|
redivcl |
|
34 |
32 33
|
syl3an1 |
|
35 |
|
opelxpi |
|
36 |
31 34 35
|
syl2anc |
|
37 |
36
|
3expb |
|
38 |
20 30 37
|
syl2an |
|
39 |
38
|
rgen2 |
|
40 |
|
eqid |
|
41 |
40
|
fmpo |
|
42 |
39 41
|
mpbi |
|
43 |
|
frn |
|
44 |
42 43
|
ax-mp |
|
45 |
19 44
|
sstri |
|
46 |
18 45
|
sstri |
|
47 |
|
rnss |
|
48 |
|
rnxpid |
|
49 |
47 48
|
sseqtrdi |
|
50 |
46 49
|
ax-mp |
|
51 |
|
rnfi |
|
52 |
|
fimaxre2 |
|
53 |
50 51 52
|
sylancr |
|
54 |
53
|
adantl |
|
55 |
|
eluni2 |
|
56 |
|
iccf |
|
57 |
|
ffn |
|
58 |
56 57
|
ax-mp |
|
59 |
|
rexpssxrxp |
|
60 |
46 59
|
sstri |
|
61 |
|
eleq2 |
|
62 |
61
|
rexima |
|
63 |
58 60 62
|
mp2an |
|
64 |
55 63
|
bitri |
|
65 |
46
|
sseli |
|
66 |
|
1st2nd2 |
|
67 |
66
|
fveq2d |
|
68 |
|
df-ov |
|
69 |
67 68
|
eqtr4di |
|
70 |
69
|
eleq2d |
|
71 |
65 70
|
syl |
|
72 |
71
|
biimpd |
|
73 |
72
|
imdistani |
|
74 |
|
eliccxr |
|
75 |
74
|
ad2antll |
|
76 |
|
xp2nd |
|
77 |
76
|
rexrd |
|
78 |
65 77
|
syl |
|
79 |
78
|
ad2antrl |
|
80 |
|
simpllr |
|
81 |
80
|
rexrd |
|
82 |
|
xp1st |
|
83 |
82
|
rexrd |
|
84 |
83 77
|
jca |
|
85 |
65 84
|
syl |
|
86 |
|
iccleub |
|
87 |
86
|
3expa |
|
88 |
85 87
|
sylan |
|
89 |
88
|
adantl |
|
90 |
|
xpss |
|
91 |
46 90
|
sstri |
|
92 |
|
df-rel |
|
93 |
91 92
|
mpbir |
|
94 |
|
2ndrn |
|
95 |
93 94
|
mpan |
|
96 |
|
breq1 |
|
97 |
96
|
rspccva |
|
98 |
95 97
|
sylan2 |
|
99 |
98
|
ad2ant2lr |
|
100 |
75 79 81 89 99
|
xrletrd |
|
101 |
73 100
|
sylan2 |
|
102 |
101
|
rexlimdvaa |
|
103 |
64 102
|
syl5bi |
|
104 |
103
|
ralrimiv |
|
105 |
|
raleq |
|
106 |
105
|
ad2antrr |
|
107 |
104 106
|
mpbid |
|
108 |
107
|
ex |
|
109 |
108
|
reximdva |
|
110 |
109
|
adantr |
|
111 |
54 110
|
mpd |
|
112 |
17 111
|
nsyl |
|
113 |
112
|
adantl |
|
114 |
|
uniretop |
|
115 |
|
retopconn |
|
116 |
115
|
a1i |
|
117 |
|
simpll |
|
118 |
|
simplr |
|
119 |
|
simprl |
|
120 |
|
ffun |
|
121 |
|
funiunfv |
|
122 |
56 120 121
|
mp2b |
|
123 |
|
retop |
|
124 |
46
|
sseli |
|
125 |
|
1st2nd2 |
|
126 |
125
|
fveq2d |
|
127 |
|
df-ov |
|
128 |
126 127
|
eqtr4di |
|
129 |
|
xp1st |
|
130 |
|
xp2nd |
|
131 |
|
icccld |
|
132 |
129 130 131
|
syl2anc |
|
133 |
128 132
|
eqeltrd |
|
134 |
124 133
|
syl |
|
135 |
134
|
rgen |
|
136 |
114
|
iuncld |
|
137 |
123 135 136
|
mp3an13 |
|
138 |
122 137
|
eqeltrrid |
|
139 |
138
|
ad2antll |
|
140 |
119 139
|
eqeltrrd |
|
141 |
114 116 117 118 140
|
connclo |
|
142 |
141
|
ex |
|
143 |
142
|
necon3ad |
|
144 |
143
|
imp |
|
145 |
113 144
|
pm2.61dane |
|
146 |
|
oveq1 |
|
147 |
|
oveq1 |
|
148 |
147
|
oveq1d |
|
149 |
146 148
|
opeq12d |
|
150 |
|
oveq2 |
|
151 |
150
|
oveq2d |
|
152 |
150
|
oveq2d |
|
153 |
151 152
|
opeq12d |
|
154 |
149 153
|
cbvmpov |
|
155 |
|
fveq2 |
|
156 |
155
|
sseq1d |
|
157 |
|
equequ1 |
|
158 |
156 157
|
imbi12d |
|
159 |
158
|
ralbidv |
|
160 |
159
|
cbvrabv |
|
161 |
19
|
a1i |
|
162 |
154 160 161
|
dyadmbllem |
|
163 |
|
opnmbllem0 |
|
164 |
162 163
|
eqtr3d |
|
165 |
164
|
adantr |
|
166 |
|
nnenom |
|
167 |
|
sdomentr |
|
168 |
166 167
|
mpan2 |
|
169 |
|
isfinite |
|
170 |
168 169
|
sylibr |
|
171 |
165 170
|
anim12i |
|
172 |
145 171
|
mtand |
|
173 |
|
qex |
|
174 |
173 173
|
xpex |
|
175 |
|
zq |
|
176 |
|
2nn |
|
177 |
|
nnq |
|
178 |
176 177
|
ax-mp |
|
179 |
|
qexpcl |
|
180 |
178 179
|
mpan |
|
181 |
180 29
|
jca |
|
182 |
|
qdivcl |
|
183 |
|
1z |
|
184 |
|
zq |
|
185 |
183 184
|
ax-mp |
|
186 |
|
qaddcl |
|
187 |
185 186
|
mpan2 |
|
188 |
|
qdivcl |
|
189 |
187 188
|
syl3an1 |
|
190 |
|
opelxpi |
|
191 |
182 189 190
|
syl2anc |
|
192 |
191
|
3expb |
|
193 |
175 181 192
|
syl2an |
|
194 |
193
|
rgen2 |
|
195 |
40
|
fmpo |
|
196 |
194 195
|
mpbi |
|
197 |
|
frn |
|
198 |
196 197
|
ax-mp |
|
199 |
19 198
|
sstri |
|
200 |
18 199
|
sstri |
|
201 |
|
ssdomg |
|
202 |
174 200 201
|
mp2 |
|
203 |
|
qnnen |
|
204 |
|
xpen |
|
205 |
203 203 204
|
mp2an |
|
206 |
|
xpnnen |
|
207 |
205 206
|
entri |
|
208 |
|
domentr |
|
209 |
202 207 208
|
mp2an |
|
210 |
172 209
|
jctil |
|
211 |
|
bren2 |
|
212 |
210 211
|
sylibr |
|
213 |
212
|
ensymd |
|
214 |
|
bren |
|
215 |
213 214
|
sylib |
|