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 |
|