Step |
Hyp |
Ref |
Expression |
1 |
|
mbfposadd.1 |
|
2 |
|
mbfposadd.2 |
|
3 |
|
mbfposadd.3 |
|
4 |
|
mbfposadd.4 |
|
5 |
|
mbfposadd.5 |
|
6 |
|
0re |
|
7 |
|
ifcl |
|
8 |
2 6 7
|
sylancl |
|
9 |
|
ifcl |
|
10 |
4 6 9
|
sylancl |
|
11 |
8 10
|
readdcld |
|
12 |
11
|
fmpttd |
|
13 |
|
ssrab2 |
|
14 |
|
fssres |
|
15 |
12 13 14
|
sylancl |
|
16 |
|
inss2 |
|
17 |
|
resabs1 |
|
18 |
16 17
|
ax-mp |
|
19 |
|
elin |
|
20 |
|
rabid |
|
21 |
|
rabid |
|
22 |
20 21
|
anbi12i |
|
23 |
19 22
|
bitri |
|
24 |
|
iftrue |
|
25 |
|
iftrue |
|
26 |
24 25
|
oveqan12d |
|
27 |
26
|
ad2ant2l |
|
28 |
23 27
|
sylbi |
|
29 |
28
|
mpteq2ia |
|
30 |
|
inss1 |
|
31 |
|
ssrab2 |
|
32 |
30 31
|
sstri |
|
33 |
|
resmpt |
|
34 |
|
nfcv |
|
35 |
|
nfcsb1v |
|
36 |
|
csbeq1a |
|
37 |
34 35 36
|
cbvmpt |
|
38 |
37
|
reseq1i |
|
39 |
|
nfv |
|
40 |
|
nfrab1 |
|
41 |
|
nfrab1 |
|
42 |
40 41
|
nfin |
|
43 |
42
|
nfcri |
|
44 |
35
|
nfeq2 |
|
45 |
43 44
|
nfan |
|
46 |
|
eleq1w |
|
47 |
36
|
eqeq2d |
|
48 |
46 47
|
anbi12d |
|
49 |
39 45 48
|
cbvopab1 |
|
50 |
|
df-mpt |
|
51 |
|
df-mpt |
|
52 |
49 50 51
|
3eqtr4i |
|
53 |
33 38 52
|
3eqtr4g |
|
54 |
32 53
|
ax-mp |
|
55 |
|
resmpt |
|
56 |
|
nfcv |
|
57 |
|
nfcsb1v |
|
58 |
|
csbeq1a |
|
59 |
56 57 58
|
cbvmpt |
|
60 |
59
|
reseq1i |
|
61 |
|
nfv |
|
62 |
57
|
nfeq2 |
|
63 |
43 62
|
nfan |
|
64 |
58
|
eqeq2d |
|
65 |
46 64
|
anbi12d |
|
66 |
61 63 65
|
cbvopab1 |
|
67 |
|
df-mpt |
|
68 |
|
df-mpt |
|
69 |
66 67 68
|
3eqtr4i |
|
70 |
55 60 69
|
3eqtr4g |
|
71 |
32 70
|
ax-mp |
|
72 |
29 54 71
|
3eqtr4i |
|
73 |
18 72
|
eqtri |
|
74 |
2
|
biantrurd |
|
75 |
|
elrege0 |
|
76 |
74 75
|
bitr4di |
|
77 |
76
|
rabbidva |
|
78 |
|
0xr |
|
79 |
|
pnfxr |
|
80 |
|
0ltpnf |
|
81 |
|
snunioo |
|
82 |
78 79 80 81
|
mp3an |
|
83 |
82
|
imaeq2i |
|
84 |
|
imaundi |
|
85 |
|
eqid |
|
86 |
85
|
mptpreima |
|
87 |
83 84 86
|
3eqtr3ri |
|
88 |
77 87
|
eqtrdi |
|
89 |
2
|
fmpttd |
|
90 |
|
mbfimasn |
|
91 |
6 90
|
mp3an3 |
|
92 |
|
mbfima |
|
93 |
|
unmbl |
|
94 |
91 92 93
|
syl2anc |
|
95 |
1 89 94
|
syl2anc |
|
96 |
88 95
|
eqeltrd |
|
97 |
4
|
biantrurd |
|
98 |
|
elrege0 |
|
99 |
97 98
|
bitr4di |
|
100 |
99
|
rabbidva |
|
101 |
82
|
imaeq2i |
|
102 |
|
imaundi |
|
103 |
|
eqid |
|
104 |
103
|
mptpreima |
|
105 |
101 102 104
|
3eqtr3ri |
|
106 |
100 105
|
eqtrdi |
|
107 |
4
|
fmpttd |
|
108 |
|
mbfimasn |
|
109 |
6 108
|
mp3an3 |
|
110 |
|
mbfima |
|
111 |
|
unmbl |
|
112 |
109 110 111
|
syl2anc |
|
113 |
3 107 112
|
syl2anc |
|
114 |
106 113
|
eqeltrd |
|
115 |
|
inmbl |
|
116 |
96 114 115
|
syl2anc |
|
117 |
|
mbfres |
|
118 |
5 116 117
|
syl2anc |
|
119 |
73 118
|
eqeltrid |
|
120 |
|
inss2 |
|
121 |
|
resabs1 |
|
122 |
120 121
|
ax-mp |
|
123 |
|
rabid |
|
124 |
123 21
|
anbi12i |
|
125 |
|
elin |
|
126 |
|
anandi |
|
127 |
124 125 126
|
3bitr4i |
|
128 |
|
iffalse |
|
129 |
128 25
|
oveqan12d |
|
130 |
129
|
ad2antll |
|
131 |
4
|
recnd |
|
132 |
131
|
addid2d |
|
133 |
132
|
adantrr |
|
134 |
130 133
|
eqtrd |
|
135 |
127 134
|
sylan2b |
|
136 |
135
|
mpteq2dva |
|
137 |
|
inss1 |
|
138 |
|
ssrab2 |
|
139 |
137 138
|
sstri |
|
140 |
|
resmpt |
|
141 |
37
|
reseq1i |
|
142 |
|
nfv |
|
143 |
|
nfrab1 |
|
144 |
143 41
|
nfin |
|
145 |
144
|
nfcri |
|
146 |
145 44
|
nfan |
|
147 |
|
eleq1w |
|
148 |
147 47
|
anbi12d |
|
149 |
142 146 148
|
cbvopab1 |
|
150 |
|
df-mpt |
|
151 |
|
df-mpt |
|
152 |
149 150 151
|
3eqtr4i |
|
153 |
140 141 152
|
3eqtr4g |
|
154 |
139 153
|
ax-mp |
|
155 |
|
resmpt |
|
156 |
|
nfcv |
|
157 |
|
nfcsb1v |
|
158 |
|
csbeq1a |
|
159 |
156 157 158
|
cbvmpt |
|
160 |
159
|
reseq1i |
|
161 |
|
nfv |
|
162 |
157
|
nfeq2 |
|
163 |
145 162
|
nfan |
|
164 |
158
|
eqeq2d |
|
165 |
147 164
|
anbi12d |
|
166 |
161 163 165
|
cbvopab1 |
|
167 |
|
df-mpt |
|
168 |
|
df-mpt |
|
169 |
166 167 168
|
3eqtr4i |
|
170 |
155 160 169
|
3eqtr4g |
|
171 |
139 170
|
ax-mp |
|
172 |
136 154 171
|
3eqtr4g |
|
173 |
122 172
|
syl5eq |
|
174 |
85
|
mptpreima |
|
175 |
|
elioomnf |
|
176 |
78 175
|
ax-mp |
|
177 |
2
|
biantrurd |
|
178 |
|
ltnle |
|
179 |
2 6 178
|
sylancl |
|
180 |
177 179
|
bitr3d |
|
181 |
176 180
|
syl5bb |
|
182 |
181
|
rabbidva |
|
183 |
174 182
|
syl5eq |
|
184 |
|
mbfima |
|
185 |
1 89 184
|
syl2anc |
|
186 |
183 185
|
eqeltrrd |
|
187 |
|
inmbl |
|
188 |
186 114 187
|
syl2anc |
|
189 |
|
mbfres |
|
190 |
3 188 189
|
syl2anc |
|
191 |
173 190
|
eqeltrd |
|
192 |
|
ssid |
|
193 |
|
dfrab3ss |
|
194 |
192 193
|
ax-mp |
|
195 |
|
rabxm |
|
196 |
195
|
ineq1i |
|
197 |
|
indir |
|
198 |
194 196 197
|
3eqtrri |
|
199 |
198
|
a1i |
|
200 |
15 119 191 199
|
mbfres2 |
|
201 |
|
rabid |
|
202 |
|
iffalse |
|
203 |
202
|
oveq2d |
|
204 |
8
|
recnd |
|
205 |
204
|
addid1d |
|
206 |
203 205
|
sylan9eqr |
|
207 |
206
|
anasss |
|
208 |
201 207
|
sylan2b |
|
209 |
208
|
mpteq2dva |
|
210 |
|
ssrab2 |
|
211 |
|
resmpt |
|
212 |
37
|
reseq1i |
|
213 |
|
nfv |
|
214 |
|
nfrab1 |
|
215 |
214
|
nfcri |
|
216 |
215 44
|
nfan |
|
217 |
|
eleq1w |
|
218 |
217 47
|
anbi12d |
|
219 |
213 216 218
|
cbvopab1 |
|
220 |
|
df-mpt |
|
221 |
|
df-mpt |
|
222 |
219 220 221
|
3eqtr4i |
|
223 |
211 212 222
|
3eqtr4g |
|
224 |
210 223
|
ax-mp |
|
225 |
|
resmpt |
|
226 |
|
nfcv |
|
227 |
|
nfcsb1v |
|
228 |
|
csbeq1a |
|
229 |
226 227 228
|
cbvmpt |
|
230 |
229
|
reseq1i |
|
231 |
|
nfv |
|
232 |
227
|
nfeq2 |
|
233 |
215 232
|
nfan |
|
234 |
228
|
eqeq2d |
|
235 |
217 234
|
anbi12d |
|
236 |
231 233 235
|
cbvopab1 |
|
237 |
|
df-mpt |
|
238 |
|
df-mpt |
|
239 |
236 237 238
|
3eqtr4i |
|
240 |
225 230 239
|
3eqtr4g |
|
241 |
210 240
|
ax-mp |
|
242 |
209 224 241
|
3eqtr4g |
|
243 |
2 1
|
mbfpos |
|
244 |
103
|
mptpreima |
|
245 |
|
elioomnf |
|
246 |
78 245
|
ax-mp |
|
247 |
4
|
biantrurd |
|
248 |
|
ltnle |
|
249 |
4 6 248
|
sylancl |
|
250 |
247 249
|
bitr3d |
|
251 |
246 250
|
syl5bb |
|
252 |
251
|
rabbidva |
|
253 |
244 252
|
syl5eq |
|
254 |
|
mbfima |
|
255 |
3 107 254
|
syl2anc |
|
256 |
253 255
|
eqeltrrd |
|
257 |
|
mbfres |
|
258 |
243 256 257
|
syl2anc |
|
259 |
242 258
|
eqeltrd |
|
260 |
|
rabxm |
|
261 |
260
|
eqcomi |
|
262 |
261
|
a1i |
|
263 |
12 200 259 262
|
mbfres2 |
|