Step |
Hyp |
Ref |
Expression |
1 |
|
aomclem8.a |
|
2 |
|
aomclem8.y |
|
3 |
|
elequ2 |
|
4 |
|
elequ2 |
|
5 |
4
|
notbid |
|
6 |
3 5
|
bi2anan9r |
|
7 |
|
elequ2 |
|
8 |
|
elequ2 |
|
9 |
7 8
|
bi2bian9 |
|
10 |
9
|
imbi2d |
|
11 |
10
|
ralbidv |
|
12 |
6 11
|
anbi12d |
|
13 |
12
|
rexbidv |
|
14 |
|
elequ1 |
|
15 |
|
elequ1 |
|
16 |
15
|
notbid |
|
17 |
14 16
|
anbi12d |
|
18 |
|
breq2 |
|
19 |
18
|
imbi1d |
|
20 |
19
|
ralbidv |
|
21 |
|
breq1 |
|
22 |
|
elequ1 |
|
23 |
|
elequ1 |
|
24 |
22 23
|
bibi12d |
|
25 |
21 24
|
imbi12d |
|
26 |
25
|
cbvralvw |
|
27 |
20 26
|
bitrdi |
|
28 |
17 27
|
anbi12d |
|
29 |
28
|
cbvrexvw |
|
30 |
13 29
|
bitrdi |
|
31 |
30
|
cbvopabv |
|
32 |
|
nfcv |
|
33 |
|
nfcv |
|
34 |
|
nfcv |
|
35 |
|
nfopab1 |
|
36 |
33 34 35
|
nfsup |
|
37 |
|
fveq2 |
|
38 |
37
|
supeq1d |
|
39 |
32 36 38
|
cbvmpt |
|
40 |
|
nfcv |
|
41 |
|
nffvmpt1 |
|
42 |
|
rneq |
|
43 |
42
|
difeq2d |
|
44 |
43
|
fveq2d |
|
45 |
40 41 44
|
cbvmpt |
|
46 |
|
recseq |
|
47 |
45 46
|
ax-mp |
|
48 |
|
nfv |
|
49 |
|
nfv |
|
50 |
|
nfmpt1 |
|
51 |
50
|
nfrecs |
|
52 |
51
|
nfcnv |
|
53 |
|
nfcv |
|
54 |
52 53
|
nfima |
|
55 |
54
|
nfint |
|
56 |
|
nfcv |
|
57 |
52 56
|
nfima |
|
58 |
57
|
nfint |
|
59 |
55 58
|
nfel |
|
60 |
|
nfcv |
|
61 |
|
nfcv |
|
62 |
|
nfcv |
|
63 |
|
nfopab2 |
|
64 |
61 62 63
|
nfsup |
|
65 |
60 64
|
nfmpt |
|
66 |
|
nfcv |
|
67 |
65 66
|
nffv |
|
68 |
60 67
|
nfmpt |
|
69 |
68
|
nfrecs |
|
70 |
69
|
nfcnv |
|
71 |
|
nfcv |
|
72 |
70 71
|
nfima |
|
73 |
72
|
nfint |
|
74 |
|
nfcv |
|
75 |
70 74
|
nfima |
|
76 |
75
|
nfint |
|
77 |
73 76
|
nfel |
|
78 |
|
sneq |
|
79 |
78
|
imaeq2d |
|
80 |
79
|
inteqd |
|
81 |
|
sneq |
|
82 |
81
|
imaeq2d |
|
83 |
82
|
inteqd |
|
84 |
|
eleq12 |
|
85 |
80 83 84
|
syl2an |
|
86 |
48 49 59 77 85
|
cbvopab |
|
87 |
|
fveq2 |
|
88 |
|
fveq2 |
|
89 |
87 88
|
breqan12d |
|
90 |
87 88
|
eqeqan12d |
|
91 |
|
simpl |
|
92 |
|
suceq |
|
93 |
87 92
|
syl |
|
94 |
93
|
adantr |
|
95 |
94
|
fveq2d |
|
96 |
|
simpr |
|
97 |
91 95 96
|
breq123d |
|
98 |
90 97
|
anbi12d |
|
99 |
89 98
|
orbi12d |
|
100 |
99
|
cbvopabv |
|
101 |
|
eqid |
|
102 |
|
dmeq |
|
103 |
102
|
unieqd |
|
104 |
102 103
|
eqeq12d |
|
105 |
|
fveq1 |
|
106 |
105
|
breqd |
|
107 |
106
|
anbi2d |
|
108 |
107
|
orbi2d |
|
109 |
108
|
opabbidv |
|
110 |
|
eqidd |
|
111 |
102
|
fveq2d |
|
112 |
103
|
fveq2d |
|
113 |
|
id |
|
114 |
113 103
|
fveq12d |
|
115 |
114
|
breqd |
|
116 |
115
|
imbi1d |
|
117 |
112 116
|
raleqbidv |
|
118 |
117
|
anbi2d |
|
119 |
112 118
|
rexeqbidv |
|
120 |
119
|
opabbidv |
|
121 |
110 111 120
|
supeq123d |
|
122 |
121
|
mpteq2dv |
|
123 |
111
|
difeq1d |
|
124 |
122 123
|
fveq12d |
|
125 |
124
|
mpteq2dv |
|
126 |
|
recseq |
|
127 |
125 126
|
syl |
|
128 |
127
|
cnveqd |
|
129 |
128
|
imaeq1d |
|
130 |
129
|
inteqd |
|
131 |
128
|
imaeq1d |
|
132 |
131
|
inteqd |
|
133 |
130 132
|
eleq12d |
|
134 |
133
|
opabbidv |
|
135 |
104 109 134
|
ifbieq12d |
|
136 |
111
|
sqxpeqd |
|
137 |
135 136
|
ineq12d |
|
138 |
137
|
cbvmptv |
|
139 |
|
recseq |
|
140 |
138 139
|
ax-mp |
|
141 |
|
neeq1 |
|
142 |
|
fveq2 |
|
143 |
|
pweq |
|
144 |
143
|
ineq1d |
|
145 |
144
|
difeq1d |
|
146 |
142 145
|
eleq12d |
|
147 |
141 146
|
imbi12d |
|
148 |
147
|
cbvralvw |
|
149 |
2 148
|
sylib |
|
150 |
31 39 47 86 100 101 140 1 149
|
aomclem7 |
|