Step |
Hyp |
Ref |
Expression |
1 |
|
fveq2 |
|
2 |
|
fveq2 |
|
3 |
1 2
|
oveqan12d |
|
4 |
3
|
eqeq2d |
|
5 |
|
fveq2 |
|
6 |
|
fveq2 |
|
7 |
5 6
|
ineqan12d |
|
8 |
7
|
difeq2d |
|
9 |
8
|
eqeq2d |
|
10 |
4 9
|
anbi12d |
|
11 |
10
|
cbvrexdva |
|
12 |
|
simpr |
|
13 |
1
|
adantr |
|
14 |
12 13
|
goaleq12d |
|
15 |
14
|
eqeq2d |
|
16 |
|
opeq1 |
|
17 |
16
|
sneqd |
|
18 |
|
sneq |
|
19 |
18
|
difeq2d |
|
20 |
19
|
reseq2d |
|
21 |
17 20
|
uneq12d |
|
22 |
21
|
adantl |
|
23 |
5
|
adantr |
|
24 |
22 23
|
eleq12d |
|
25 |
24
|
ralbidv |
|
26 |
25
|
rabbidv |
|
27 |
26
|
eqeq2d |
|
28 |
15 27
|
anbi12d |
|
29 |
28
|
cbvrexdva |
|
30 |
11 29
|
orbi12d |
|
31 |
30
|
cbvrexvw |
|
32 |
|
simp-4l |
|
33 |
|
simpr |
|
34 |
33
|
anim1i |
|
35 |
|
simpr |
|
36 |
35
|
anim1i |
|
37 |
36
|
ad2antrr |
|
38 |
|
satffunlem |
|
39 |
38
|
eqcomd |
|
40 |
39
|
3exp |
|
41 |
32 34 37 40
|
syl3anc |
|
42 |
41
|
rexlimdva |
|
43 |
|
eqeq1 |
|
44 |
|
df-goal |
|
45 |
|
fvex |
|
46 |
|
fvex |
|
47 |
|
gonafv |
|
48 |
45 46 47
|
mp2an |
|
49 |
44 48
|
eqeq12i |
|
50 |
|
2oex |
|
51 |
|
opex |
|
52 |
50 51
|
opth |
|
53 |
|
1one2o |
|
54 |
|
df-ne |
|
55 |
|
pm2.21 |
|
56 |
54 55
|
sylbi |
|
57 |
53 56
|
ax-mp |
|
58 |
57
|
eqcoms |
|
59 |
58
|
adantr |
|
60 |
52 59
|
sylbi |
|
61 |
49 60
|
sylbi |
|
62 |
43 61
|
syl6bi |
|
63 |
62
|
impd |
|
64 |
63
|
adantr |
|
65 |
64
|
a1i |
|
66 |
65
|
rexlimdva |
|
67 |
42 66
|
jaod |
|
68 |
67
|
rexlimdva |
|
69 |
68
|
com23 |
|
70 |
69
|
rexlimdva |
|
71 |
|
eqeq1 |
|
72 |
|
df-goal |
|
73 |
|
fvex |
|
74 |
|
fvex |
|
75 |
|
gonafv |
|
76 |
73 74 75
|
mp2an |
|
77 |
72 76
|
eqeq12i |
|
78 |
|
opex |
|
79 |
50 78
|
opth |
|
80 |
|
pm2.21 |
|
81 |
54 80
|
sylbi |
|
82 |
53 81
|
ax-mp |
|
83 |
82
|
eqcoms |
|
84 |
83
|
adantr |
|
85 |
79 84
|
sylbi |
|
86 |
77 85
|
sylbi |
|
87 |
71 86
|
syl6bi |
|
88 |
87
|
adantr |
|
89 |
88
|
com12 |
|
90 |
89
|
adantr |
|
91 |
90
|
a1i |
|
92 |
91
|
rexlimdva |
|
93 |
|
eqeq1 |
|
94 |
44 72
|
eqeq12i |
|
95 |
50 51
|
opth |
|
96 |
|
vex |
|
97 |
96 73
|
opth |
|
98 |
97
|
anbi2i |
|
99 |
94 95 98
|
3bitri |
|
100 |
93 99
|
syl6bb |
|
101 |
100
|
adantl |
|
102 |
|
funfv1st2nd |
|
103 |
102
|
ex |
|
104 |
|
funfv1st2nd |
|
105 |
104
|
ex |
|
106 |
|
fveqeq2 |
|
107 |
|
eqtr2 |
|
108 |
|
opeq1 |
|
109 |
108
|
sneqd |
|
110 |
|
sneq |
|
111 |
110
|
difeq2d |
|
112 |
111
|
reseq2d |
|
113 |
109 112
|
uneq12d |
|
114 |
113
|
eqcoms |
|
115 |
114
|
adantl |
|
116 |
|
simpl |
|
117 |
116
|
eqcomd |
|
118 |
115 117
|
eleq12d |
|
119 |
118
|
ralbidv |
|
120 |
119
|
rabbidv |
|
121 |
|
eqeq12 |
|
122 |
120 121
|
syl5ibrcom |
|
123 |
122
|
exp4b |
|
124 |
107 123
|
syl |
|
125 |
124
|
ex |
|
126 |
106 125
|
syl6bi |
|
127 |
126
|
com24 |
|
128 |
127
|
impcom |
|
129 |
128
|
com13 |
|
130 |
105 129
|
syl6 |
|
131 |
130
|
com23 |
|
132 |
103 131
|
syld |
|
133 |
132
|
imp |
|
134 |
133
|
adantr |
|
135 |
134
|
imp |
|
136 |
135
|
adantld |
|
137 |
136
|
ad2antrr |
|
138 |
101 137
|
sylbid |
|
139 |
138
|
impd |
|
140 |
139
|
ex |
|
141 |
140
|
com34 |
|
142 |
141
|
impd |
|
143 |
142
|
rexlimdva |
|
144 |
92 143
|
jaod |
|
145 |
144
|
rexlimdva |
|
146 |
145
|
com23 |
|
147 |
146
|
rexlimdva |
|
148 |
70 147
|
jaod |
|
149 |
148
|
rexlimdva |
|
150 |
31 149
|
syl5bi |
|
151 |
150
|
impd |
|
152 |
151
|
alrimivv |
|
153 |
|
eqeq1 |
|
154 |
153
|
anbi2d |
|
155 |
154
|
rexbidv |
|
156 |
|
eqeq1 |
|
157 |
156
|
anbi2d |
|
158 |
157
|
rexbidv |
|
159 |
155 158
|
orbi12d |
|
160 |
159
|
rexbidv |
|
161 |
160
|
mo4 |
|
162 |
152 161
|
sylibr |
|
163 |
162
|
alrimiv |
|
164 |
|
funopab |
|
165 |
163 164
|
sylibr |
|