| Step |
Hyp |
Ref |
Expression |
| 1 |
|
f1ounsn.f |
|
| 2 |
|
f1of |
|
| 3 |
|
ssun1 |
|
| 4 |
3
|
a1i |
|
| 5 |
2 4
|
fssd |
|
| 6 |
5
|
3ad2ant1 |
|
| 7 |
|
simpl |
|
| 8 |
|
df-nel |
|
| 9 |
8
|
biimpi |
|
| 10 |
9
|
adantr |
|
| 11 |
7 10
|
anim12i |
|
| 12 |
11
|
3adant1 |
|
| 13 |
|
eqid |
|
| 14 |
13
|
olci |
|
| 15 |
|
elunsn |
|
| 16 |
14 15
|
mpbiri |
|
| 17 |
16
|
adantl |
|
| 18 |
17
|
3ad2ant2 |
|
| 19 |
6 12 18
|
3jca |
|
| 20 |
|
fsnunf |
|
| 21 |
19 20
|
syl |
|
| 22 |
|
f1of1 |
|
| 23 |
|
dff14a |
|
| 24 |
|
neeq1 |
|
| 25 |
|
fveq2 |
|
| 26 |
25
|
neeq1d |
|
| 27 |
24 26
|
imbi12d |
|
| 28 |
|
neeq2 |
|
| 29 |
|
fveq2 |
|
| 30 |
29
|
neeq2d |
|
| 31 |
28 30
|
imbi12d |
|
| 32 |
27 31
|
rspc2va |
|
| 33 |
32
|
expcom |
|
| 34 |
33
|
adantl |
|
| 35 |
23 34
|
sylbi |
|
| 36 |
22 35
|
syl |
|
| 37 |
36
|
3ad2ant1 |
|
| 38 |
37
|
impl |
|
| 39 |
38
|
imp |
|
| 40 |
|
nelne2 |
|
| 41 |
40
|
necomd |
|
| 42 |
41
|
expcom |
|
| 43 |
8 42
|
sylbi |
|
| 44 |
43
|
adantr |
|
| 45 |
44
|
3ad2ant3 |
|
| 46 |
45
|
imp |
|
| 47 |
46
|
adantr |
|
| 48 |
47
|
adantr |
|
| 49 |
|
fvunsn |
|
| 50 |
48 49
|
syl |
|
| 51 |
|
nelne2 |
|
| 52 |
51
|
necomd |
|
| 53 |
52
|
expcom |
|
| 54 |
8 53
|
sylbi |
|
| 55 |
54
|
adantr |
|
| 56 |
55
|
3ad2ant3 |
|
| 57 |
56
|
adantr |
|
| 58 |
57
|
imp |
|
| 59 |
58
|
adantr |
|
| 60 |
|
fvunsn |
|
| 61 |
59 60
|
syl |
|
| 62 |
39 50 61
|
3netr4d |
|
| 63 |
62
|
ex |
|
| 64 |
63
|
ralrimiva |
|
| 65 |
2
|
3ad2ant1 |
|
| 66 |
65
|
ffvelcdmda |
|
| 67 |
|
df-nel |
|
| 68 |
67
|
biimpi |
|
| 69 |
68
|
adantl |
|
| 70 |
69
|
3ad2ant3 |
|
| 71 |
70
|
adantr |
|
| 72 |
|
nelne2 |
|
| 73 |
66 71 72
|
syl2anc |
|
| 74 |
73
|
adantr |
|
| 75 |
|
simpr |
|
| 76 |
75
|
necomd |
|
| 77 |
76 49
|
syl |
|
| 78 |
7
|
3ad2ant2 |
|
| 79 |
|
simpr |
|
| 80 |
79
|
3ad2ant2 |
|
| 81 |
|
f1odm |
|
| 82 |
81
|
eqcomd |
|
| 83 |
82
|
eleq2d |
|
| 84 |
83
|
notbid |
|
| 85 |
8 84
|
bitrid |
|
| 86 |
85
|
biimpd |
|
| 87 |
86
|
adantrd |
|
| 88 |
87
|
imp |
|
| 89 |
88
|
3adant2 |
|
| 90 |
78 80 89
|
3jca |
|
| 91 |
90
|
adantr |
|
| 92 |
91
|
adantr |
|
| 93 |
|
fsnunfv |
|
| 94 |
92 93
|
syl |
|
| 95 |
74 77 94
|
3netr4d |
|
| 96 |
95
|
ex |
|
| 97 |
78
|
adantr |
|
| 98 |
|
neeq2 |
|
| 99 |
|
fveq2 |
|
| 100 |
99
|
neeq2d |
|
| 101 |
98 100
|
imbi12d |
|
| 102 |
101
|
ralsng |
|
| 103 |
97 102
|
syl |
|
| 104 |
96 103
|
mpbird |
|
| 105 |
|
ralun |
|
| 106 |
64 104 105
|
syl2anc |
|
| 107 |
106
|
ralrimiva |
|
| 108 |
65
|
ffvelcdmda |
|
| 109 |
70
|
adantr |
|
| 110 |
108 109
|
jca |
|
| 111 |
110
|
adantr |
|
| 112 |
|
nelne2 |
|
| 113 |
112
|
necomd |
|
| 114 |
111 113
|
syl |
|
| 115 |
90
|
adantr |
|
| 116 |
115
|
adantr |
|
| 117 |
116 93
|
syl |
|
| 118 |
60
|
adantl |
|
| 119 |
114 117 118
|
3netr4d |
|
| 120 |
119
|
ex |
|
| 121 |
120
|
ralrimiva |
|
| 122 |
|
eqid |
|
| 123 |
|
eqneqall |
|
| 124 |
122 123
|
ax-mp |
|
| 125 |
|
neeq2 |
|
| 126 |
99
|
neeq2d |
|
| 127 |
125 126
|
imbi12d |
|
| 128 |
127
|
ralsng |
|
| 129 |
78 128
|
syl |
|
| 130 |
124 129
|
mpbiri |
|
| 131 |
|
ralun |
|
| 132 |
121 130 131
|
syl2anc |
|
| 133 |
|
neeq1 |
|
| 134 |
|
fveq2 |
|
| 135 |
134
|
neeq1d |
|
| 136 |
133 135
|
imbi12d |
|
| 137 |
136
|
ralbidv |
|
| 138 |
137
|
ralsng |
|
| 139 |
78 138
|
syl |
|
| 140 |
132 139
|
mpbird |
|
| 141 |
|
ralun |
|
| 142 |
107 140 141
|
syl2anc |
|
| 143 |
21 142
|
jca |
|
| 144 |
|
rnun |
|
| 145 |
|
f1ofo |
|
| 146 |
|
forn |
|
| 147 |
145 146
|
syl |
|
| 148 |
147
|
3ad2ant1 |
|
| 149 |
|
rnsnopg |
|
| 150 |
149
|
adantr |
|
| 151 |
150
|
3ad2ant2 |
|
| 152 |
148 151
|
uneq12d |
|
| 153 |
144 152
|
eqtrid |
|
| 154 |
143 153
|
jca |
|
| 155 |
|
dff1o5 |
|
| 156 |
|
dff14a |
|
| 157 |
155 156
|
bianbi |
|
| 158 |
154 157
|
sylibr |
|
| 159 |
|
f1oeq1 |
|
| 160 |
1 159
|
ax-mp |
|
| 161 |
158 160
|
sylibr |
|