Step |
Hyp |
Ref |
Expression |
1 |
|
dfac3 |
|
2 |
|
nfra1 |
|
3 |
|
rsp |
|
4 |
|
equid |
|
5 |
|
neeq1 |
|
6 |
|
eqeq1 |
|
7 |
5 6
|
anbi12d |
|
8 |
7
|
rspcev |
|
9 |
4 8
|
mpanr2 |
|
10 |
|
fveq2 |
|
11 |
10
|
preq1d |
|
12 |
|
preq2 |
|
13 |
11 12
|
eqtr2d |
|
14 |
13
|
anim2i |
|
15 |
14
|
reximi |
|
16 |
9 15
|
syl |
|
17 |
|
prex |
|
18 |
|
eqeq1 |
|
19 |
18
|
anbi2d |
|
20 |
19
|
rexbidv |
|
21 |
17 20
|
elab |
|
22 |
16 21
|
sylibr |
|
23 |
|
vex |
|
24 |
23
|
prid2 |
|
25 |
|
fvex |
|
26 |
25
|
prid1 |
|
27 |
24 26
|
pm3.2i |
|
28 |
|
eleq2 |
|
29 |
|
eleq2 |
|
30 |
28 29
|
anbi12d |
|
31 |
30
|
rspcev |
|
32 |
22 27 31
|
sylancl |
|
33 |
|
eleq1 |
|
34 |
|
eleq1 |
|
35 |
34
|
anbi2d |
|
36 |
35
|
rexbidv |
|
37 |
33 36
|
anbi12d |
|
38 |
25 37
|
spcev |
|
39 |
32 38
|
sylan2 |
|
40 |
39
|
ex |
|
41 |
3 40
|
syl8 |
|
42 |
41
|
impd |
|
43 |
42
|
pm2.43d |
|
44 |
|
df-rex |
|
45 |
|
vex |
|
46 |
|
eqeq1 |
|
47 |
46
|
anbi2d |
|
48 |
47
|
rexbidv |
|
49 |
45 48
|
elab |
|
50 |
|
neeq1 |
|
51 |
|
fveq2 |
|
52 |
51
|
eleq1d |
|
53 |
|
eleq2 |
|
54 |
52 53
|
bitrd |
|
55 |
50 54
|
imbi12d |
|
56 |
55
|
rspccv |
|
57 |
|
elneq |
|
58 |
57
|
neneqd |
|
59 |
|
vex |
|
60 |
|
neqne |
|
61 |
|
prel12g |
|
62 |
59 23 60 61
|
mp3an12i |
|
63 |
|
eleq2 |
|
64 |
|
eleq2 |
|
65 |
63 64
|
anbi12d |
|
66 |
|
ancom |
|
67 |
65 66
|
bitr3di |
|
68 |
62 67
|
sylan9bbr |
|
69 |
58 68
|
sylan2 |
|
70 |
69
|
adantrr |
|
71 |
70
|
pm5.32da |
|
72 |
23
|
preleq |
|
73 |
71 72
|
syl6bir |
|
74 |
51
|
eqeq2d |
|
75 |
74
|
biimparc |
|
76 |
73 75
|
syl6 |
|
77 |
76
|
exp4c |
|
78 |
77
|
com13 |
|
79 |
56 78
|
syl8 |
|
80 |
79
|
com4r |
|
81 |
80
|
imp |
|
82 |
81
|
imp4a |
|
83 |
82
|
com3l |
|
84 |
83
|
rexlimiv |
|
85 |
49 84
|
sylbi |
|
86 |
85
|
expd |
|
87 |
86
|
com13 |
|
88 |
87
|
imp4b |
|
89 |
88
|
exlimdv |
|
90 |
44 89
|
syl5bi |
|
91 |
90
|
expimpd |
|
92 |
91
|
alrimiv |
|
93 |
|
mo2icl |
|
94 |
92 93
|
syl |
|
95 |
43 94
|
jctird |
|
96 |
|
df-reu |
|
97 |
|
df-eu |
|
98 |
96 97
|
bitri |
|
99 |
95 98
|
syl6ibr |
|
100 |
99
|
expd |
|
101 |
2 100
|
ralrimi |
|
102 |
|
vex |
|
103 |
102
|
rnex |
|
104 |
|
p0ex |
|
105 |
103 104
|
unex |
|
106 |
|
vex |
|
107 |
105 106
|
unex |
|
108 |
107
|
pwex |
|
109 |
|
ssun1 |
|
110 |
|
fvrn0 |
|
111 |
109 110
|
sselii |
|
112 |
|
elun2 |
|
113 |
|
prssi |
|
114 |
111 112 113
|
sylancr |
|
115 |
|
prex |
|
116 |
115
|
elpw |
|
117 |
114 116
|
sylibr |
|
118 |
|
eleq1 |
|
119 |
117 118
|
syl5ibrcom |
|
120 |
119
|
adantld |
|
121 |
120
|
rexlimiv |
|
122 |
121
|
abssi |
|
123 |
108 122
|
ssexi |
|
124 |
|
rexeq |
|
125 |
124
|
reubidv |
|
126 |
125
|
imbi2d |
|
127 |
126
|
ralbidv |
|
128 |
123 127
|
spcev |
|
129 |
101 128
|
syl |
|
130 |
129
|
exlimiv |
|
131 |
130
|
alimi |
|
132 |
1 131
|
sylbi |
|