Step |
Hyp |
Ref |
Expression |
1 |
|
isomenndlem.o |
|
2 |
|
isomenndlem.o0 |
|
3 |
|
isomenndlem.y |
|
4 |
|
isomenndlem.subadd |
|
5 |
|
isomenndlem.b |
|
6 |
|
isomenndlem.f |
|
7 |
|
isomenndlem.a |
|
8 |
|
id |
|
9 |
|
iftrue |
|
10 |
9
|
adantl |
|
11 |
|
f1of |
|
12 |
6 11
|
syl |
|
13 |
|
ssun1 |
|
14 |
13
|
a1i |
|
15 |
12 14
|
fssd |
|
16 |
15
|
ffvelrnda |
|
17 |
10 16
|
eqeltrd |
|
18 |
17
|
adantlr |
|
19 |
|
iffalse |
|
20 |
19
|
adantl |
|
21 |
|
0ex |
|
22 |
21
|
snid |
|
23 |
|
elun2 |
|
24 |
22 23
|
ax-mp |
|
25 |
24
|
a1i |
|
26 |
20 25
|
eqeltrd |
|
27 |
26
|
adantlr |
|
28 |
18 27
|
pm2.61dan |
|
29 |
28 7
|
fmptd |
|
30 |
|
0elpw |
|
31 |
|
snssi |
|
32 |
30 31
|
ax-mp |
|
33 |
32
|
a1i |
|
34 |
3 33
|
unssd |
|
35 |
29 34
|
fssd |
|
36 |
|
nnex |
|
37 |
36
|
mptex |
|
38 |
7 37
|
eqeltri |
|
39 |
|
feq1 |
|
40 |
39
|
anbi2d |
|
41 |
|
fveq1 |
|
42 |
41
|
iuneq2d |
|
43 |
42
|
fveq2d |
|
44 |
|
simpl |
|
45 |
44
|
fveq1d |
|
46 |
45
|
fveq2d |
|
47 |
46
|
mpteq2dva |
|
48 |
47
|
fveq2d |
|
49 |
43 48
|
breq12d |
|
50 |
40 49
|
imbi12d |
|
51 |
38 50 4
|
vtocl |
|
52 |
8 35 51
|
syl2anc |
|
53 |
12
|
ad2antrr |
|
54 |
|
simpr |
|
55 |
|
id |
|
56 |
55
|
eqcomd |
|
57 |
56
|
adantr |
|
58 |
54 57
|
eleqtrd |
|
59 |
58
|
adantll |
|
60 |
53 59
|
ffvelrnd |
|
61 |
|
eqid |
|
62 |
60 61
|
fmptd |
|
63 |
7
|
a1i |
|
64 |
58
|
iftrued |
|
65 |
64
|
mpteq2dva |
|
66 |
63 65
|
eqtrd |
|
67 |
66
|
feq1d |
|
68 |
67
|
adantl |
|
69 |
62 68
|
mpbird |
|
70 |
|
f1ofo |
|
71 |
6 70
|
syl |
|
72 |
|
dffo3 |
|
73 |
71 72
|
sylib |
|
74 |
73
|
simprd |
|
75 |
74
|
adantr |
|
76 |
|
simpr |
|
77 |
|
rspa |
|
78 |
75 76 77
|
syl2anc |
|
79 |
78
|
adantlr |
|
80 |
|
nfv |
|
81 |
|
nfre1 |
|
82 |
|
simpr |
|
83 |
|
simpl |
|
84 |
82 83
|
eleqtrd |
|
85 |
84
|
adantll |
|
86 |
85
|
3adant3 |
|
87 |
63
|
fveq1d |
|
88 |
87
|
3ad2ant1 |
|
89 |
|
fvex |
|
90 |
89 21
|
ifex |
|
91 |
90
|
a1i |
|
92 |
|
eqid |
|
93 |
92
|
fvmpt2 |
|
94 |
84 91 93
|
syl2anc |
|
95 |
9
|
adantl |
|
96 |
94 95
|
eqtrd |
|
97 |
96
|
3adant3 |
|
98 |
|
id |
|
99 |
98
|
eqcomd |
|
100 |
99
|
3ad2ant3 |
|
101 |
88 97 100
|
3eqtrrd |
|
102 |
101
|
3adant1l |
|
103 |
|
rspe |
|
104 |
86 102 103
|
syl2anc |
|
105 |
104
|
3exp |
|
106 |
80 81 105
|
rexlimd |
|
107 |
106
|
adantr |
|
108 |
79 107
|
mpd |
|
109 |
108
|
ralrimiva |
|
110 |
69 109
|
jca |
|
111 |
|
dffo3 |
|
112 |
110 111
|
sylibr |
|
113 |
|
founiiun |
|
114 |
112 113
|
syl |
|
115 |
|
uniun |
|
116 |
21
|
unisn |
|
117 |
116
|
uneq2i |
|
118 |
|
un0 |
|
119 |
115 117 118
|
3eqtrri |
|
120 |
119
|
a1i |
|
121 |
29
|
adantr |
|
122 |
|
nfv |
|
123 |
5
|
adantr |
|
124 |
55
|
necon3bi |
|
125 |
124
|
adantl |
|
126 |
123 125
|
jca |
|
127 |
|
df-pss |
|
128 |
126 127
|
sylibr |
|
129 |
|
pssnel |
|
130 |
128 129
|
syl |
|
131 |
130
|
adantr |
|
132 |
|
simprl |
|
133 |
|
simprl |
|
134 |
90
|
a1i |
|
135 |
7
|
fvmpt2 |
|
136 |
133 134 135
|
syl2anc |
|
137 |
136
|
adantlr |
|
138 |
19
|
ad2antll |
|
139 |
|
id |
|
140 |
139
|
eqcomd |
|
141 |
140
|
ad2antlr |
|
142 |
137 138 141
|
3eqtrrd |
|
143 |
132 142 103
|
syl2anc |
|
144 |
143
|
ex |
|
145 |
144
|
adantlr |
|
146 |
122 81 131 145
|
exlimimdd |
|
147 |
146
|
adantlr |
|
148 |
|
simplll |
|
149 |
|
simpl |
|
150 |
|
elsni |
|
151 |
150
|
con3i |
|
152 |
151
|
adantl |
|
153 |
|
elunnel2 |
|
154 |
149 152 153
|
syl2anc |
|
155 |
154
|
adantll |
|
156 |
71
|
adantr |
|
157 |
|
foelrni |
|
158 |
156 76 157
|
syl2anc |
|
159 |
|
nfv |
|
160 |
5
|
sselda |
|
161 |
160
|
3adant3 |
|
162 |
160 90 135
|
sylancl |
|
163 |
162 10
|
eqtrd |
|
164 |
163
|
3adant3 |
|
165 |
|
simp3 |
|
166 |
164 165
|
eqtr2d |
|
167 |
161 166 103
|
syl2anc |
|
168 |
167
|
3exp |
|
169 |
168
|
adantr |
|
170 |
159 81 169
|
rexlimd |
|
171 |
158 170
|
mpd |
|
172 |
148 155 171
|
syl2anc |
|
173 |
147 172
|
pm2.61dan |
|
174 |
173
|
ralrimiva |
|
175 |
121 174
|
jca |
|
176 |
|
dffo3 |
|
177 |
175 176
|
sylibr |
|
178 |
|
founiiun |
|
179 |
177 178
|
syl |
|
180 |
120 179
|
eqtrd |
|
181 |
114 180
|
pm2.61dan |
|
182 |
181
|
fveq2d |
|
183 |
|
uncom |
|
184 |
183
|
a1i |
|
185 |
|
undif |
|
186 |
5 185
|
sylib |
|
187 |
184 186
|
eqtrd |
|
188 |
187
|
eqcomd |
|
189 |
188
|
mpteq1d |
|
190 |
189
|
fveq2d |
|
191 |
|
nfv |
|
192 |
|
difexg |
|
193 |
36 192
|
ax-mp |
|
194 |
193
|
a1i |
|
195 |
36
|
a1i |
|
196 |
195 5
|
ssexd |
|
197 |
|
disjdifr |
|
198 |
197
|
a1i |
|
199 |
|
simpl |
|
200 |
|
eldifi |
|
201 |
200
|
adantl |
|
202 |
1
|
adantr |
|
203 |
35
|
ffvelrnda |
|
204 |
202 203
|
ffvelrnd |
|
205 |
199 201 204
|
syl2anc |
|
206 |
160 204
|
syldan |
|
207 |
191 194 196 198 205 206
|
sge0splitmpt |
|
208 |
|
eqid |
|
209 |
206 208
|
fmptd |
|
210 |
196 209
|
sge0xrcl |
|
211 |
210
|
xaddid2d |
|
212 |
90
|
a1i |
|
213 |
201 212 135
|
syl2anc |
|
214 |
|
eldifn |
|
215 |
214
|
adantl |
|
216 |
215
|
iffalsed |
|
217 |
213 216
|
eqtrd |
|
218 |
217
|
fveq2d |
|
219 |
199 2
|
syl |
|
220 |
218 219
|
eqtrd |
|
221 |
220
|
mpteq2dva |
|
222 |
221
|
fveq2d |
|
223 |
191 194
|
sge0z |
|
224 |
222 223
|
eqtrd |
|
225 |
224
|
oveq1d |
|
226 |
1 3
|
feqresmpt |
|
227 |
226
|
fveq2d |
|
228 |
|
nfv |
|
229 |
|
fveq2 |
|
230 |
163
|
eqcomd |
|
231 |
1
|
adantr |
|
232 |
3
|
sselda |
|
233 |
231 232
|
ffvelrnd |
|
234 |
228 191 229 196 6 230 233
|
sge0f1o |
|
235 |
|
eqidd |
|
236 |
227 234 235
|
3eqtrd |
|
237 |
211 225 236
|
3eqtr4d |
|
238 |
190 207 237
|
3eqtrrd |
|
239 |
182 238
|
breq12d |
|
240 |
52 239
|
mpbird |
|