Step |
Hyp |
Ref |
Expression |
1 |
|
iundjiun.nph |
|
2 |
|
iundjiun.z |
|
3 |
|
iundjiun.e |
|
4 |
|
iundjiun.f |
|
5 |
|
eliun |
|
6 |
5
|
biimpi |
|
7 |
6
|
adantl |
|
8 |
|
nfcv |
|
9 |
|
nfiu1 |
|
10 |
8 9
|
nfel |
|
11 |
|
simp2 |
|
12 |
|
simpl |
|
13 |
|
elfzuz |
|
14 |
2
|
eqcomi |
|
15 |
13 14
|
eleqtrdi |
|
16 |
15
|
adantl |
|
17 |
|
simpr |
|
18 |
3
|
ffvelrnda |
|
19 |
|
difexg |
|
20 |
18 19
|
syl |
|
21 |
4
|
fvmpt2 |
|
22 |
17 20 21
|
syl2anc |
|
23 |
|
difssd |
|
24 |
22 23
|
eqsstrd |
|
25 |
12 16 24
|
syl2anc |
|
26 |
25
|
3adant3 |
|
27 |
|
simp3 |
|
28 |
26 27
|
sseldd |
|
29 |
|
rspe |
|
30 |
11 28 29
|
syl2anc |
|
31 |
|
eliun |
|
32 |
30 31
|
sylibr |
|
33 |
32
|
3exp |
|
34 |
1 10 33
|
rexlimd |
|
35 |
34
|
adantr |
|
36 |
7 35
|
mpd |
|
37 |
36
|
ralrimiva |
|
38 |
|
dfss3 |
|
39 |
37 38
|
sylibr |
|
40 |
|
fzssuz |
|
41 |
40
|
a1i |
|
42 |
31
|
biimpi |
|
43 |
|
nfv |
|
44 |
|
fveq2 |
|
45 |
44
|
eleq2d |
|
46 |
43 45
|
uzwo4 |
|
47 |
41 42 46
|
syl2anc |
|
48 |
47
|
adantl |
|
49 |
|
simprl |
|
50 |
|
nfv |
|
51 |
|
nfra1 |
|
52 |
50 51
|
nfan |
|
53 |
|
elfzoelz |
|
54 |
53
|
zred |
|
55 |
54
|
adantl |
|
56 |
|
elfzelz |
|
57 |
56
|
zred |
|
58 |
57
|
adantr |
|
59 |
|
1red |
|
60 |
58 59
|
resubcld |
|
61 |
|
elfzolem1 |
|
62 |
61
|
adantl |
|
63 |
58
|
ltm1d |
|
64 |
55 60 58 62 63
|
lelttrd |
|
65 |
64
|
ad4ant24 |
|
66 |
|
simplr |
|
67 |
|
elfzel1 |
|
68 |
67
|
adantr |
|
69 |
|
elfzel2 |
|
70 |
69
|
adantr |
|
71 |
53
|
adantl |
|
72 |
68 70 71
|
3jca |
|
73 |
|
elfzole1 |
|
74 |
73
|
adantl |
|
75 |
70
|
zred |
|
76 |
|
1red |
|
77 |
57 76
|
resubcld |
|
78 |
69
|
zred |
|
79 |
57
|
ltm1d |
|
80 |
|
elfzle2 |
|
81 |
77 57 78 79 80
|
ltletrd |
|
82 |
81
|
adantr |
|
83 |
55 60 75 62 82
|
lelttrd |
|
84 |
55 75 83
|
ltled |
|
85 |
72 74 84
|
jca32 |
|
86 |
|
elfz2 |
|
87 |
85 86
|
sylibr |
|
88 |
87
|
adantlr |
|
89 |
|
rspa |
|
90 |
66 88 89
|
syl2anc |
|
91 |
90
|
adantlll |
|
92 |
65 91
|
mpd |
|
93 |
92
|
ex |
|
94 |
52 93
|
ralrimi |
|
95 |
|
ralnex |
|
96 |
94 95
|
sylib |
|
97 |
|
eliun |
|
98 |
96 97
|
sylnibr |
|
99 |
98
|
adantrl |
|
100 |
49 99
|
eldifd |
|
101 |
16 22
|
syldan |
|
102 |
101
|
eqcomd |
|
103 |
102
|
adantr |
|
104 |
100 103
|
eleqtrd |
|
105 |
104
|
ex |
|
106 |
105
|
ex |
|
107 |
1 106
|
reximdai |
|
108 |
107
|
adantr |
|
109 |
48 108
|
mpd |
|
110 |
109 5
|
sylibr |
|
111 |
39 110
|
eqelssd |
|
112 |
111
|
ralrimivw |
|
113 |
2
|
iuneqfzuz |
|
114 |
112 113
|
syl |
|
115 |
|
fveq2 |
|
116 |
|
oveq2 |
|
117 |
116
|
iuneq1d |
|
118 |
115 117
|
difeq12d |
|
119 |
118
|
cbvmptv |
|
120 |
4 119
|
eqtri |
|
121 |
|
simpllr |
|
122 |
|
simplr |
|
123 |
|
simpr |
|
124 |
2 120 121 122 123
|
iundjiunlem |
|
125 |
124
|
adantlr |
|
126 |
|
simpll |
|
127 |
|
neqne |
|
128 |
|
id |
|
129 |
128 2
|
eleqtrdi |
|
130 |
|
eluzelz |
|
131 |
129 130
|
syl |
|
132 |
131
|
zred |
|
133 |
132
|
adantl |
|
134 |
133
|
ad2antrr |
|
135 |
|
id |
|
136 |
135 2
|
eleqtrdi |
|
137 |
|
eluzelz |
|
138 |
136 137
|
syl |
|
139 |
138
|
zred |
|
140 |
139
|
ad3antrrr |
|
141 |
|
simpr |
|
142 |
133
|
adantr |
|
143 |
139
|
ad2antrr |
|
144 |
142 143
|
lenltd |
|
145 |
141 144
|
mpbird |
|
146 |
145
|
adantlr |
|
147 |
|
simplr |
|
148 |
134 140 146 147
|
leneltd |
|
149 |
127 148
|
sylanl2 |
|
150 |
149
|
ad5ant2345 |
|
151 |
|
anass |
|
152 |
|
incom |
|
153 |
152
|
a1i |
|
154 |
|
simplrr |
|
155 |
|
simplrl |
|
156 |
|
simpr |
|
157 |
2 120 154 155 156
|
iundjiunlem |
|
158 |
153 157
|
eqtrd |
|
159 |
151 158
|
sylanb |
|
160 |
126 150 159
|
syl2anc |
|
161 |
125 160
|
pm2.61dan |
|
162 |
161
|
ex |
|
163 |
|
df-or |
|
164 |
162 163
|
sylibr |
|
165 |
164
|
ralrimiva |
|
166 |
165
|
ex |
|
167 |
1 166
|
ralrimi |
|
168 |
|
nfcv |
|
169 |
|
nfmpt1 |
|
170 |
4 169
|
nfcxfr |
|
171 |
|
nfcv |
|
172 |
170 171
|
nffv |
|
173 |
|
fveq2 |
|
174 |
168 172 173
|
cbvdisj |
|
175 |
|
fveq2 |
|
176 |
175
|
disjor |
|
177 |
|
nfcv |
|
178 |
|
nfv |
|
179 |
|
nfcv |
|
180 |
170 179
|
nffv |
|
181 |
172 180
|
nfin |
|
182 |
|
nfcv |
|
183 |
181 182
|
nfeq |
|
184 |
178 183
|
nfor |
|
185 |
177 184
|
nfralw |
|
186 |
|
nfv |
|
187 |
|
equequ1 |
|
188 |
|
fveq2 |
|
189 |
188
|
ineq1d |
|
190 |
189
|
eqeq1d |
|
191 |
187 190
|
orbi12d |
|
192 |
191
|
ralbidv |
|
193 |
185 186 192
|
cbvralw |
|
194 |
174 176 193
|
3bitri |
|
195 |
167 194
|
sylibr |
|
196 |
112 114 195
|
jca31 |
|