Step |
Hyp |
Ref |
Expression |
1 |
|
f1od2.1 |
|
2 |
|
f1od2.2 |
|
3 |
|
f1od2.3 |
|
4 |
|
f1od2.4 |
|
5 |
2
|
ralrimivva |
|
6 |
1
|
fnmpo |
|
7 |
5 6
|
syl |
|
8 |
|
opelxpi |
|
9 |
3 8
|
syl |
|
10 |
9
|
ralrimiva |
|
11 |
|
eqid |
|
12 |
11
|
fnmpt |
|
13 |
10 12
|
syl |
|
14 |
|
elxp7 |
|
15 |
14
|
anbi1i |
|
16 |
|
anass |
|
17 |
4
|
sbcbidv |
|
18 |
17
|
sbcbidv |
|
19 |
|
sbcan |
|
20 |
|
sbcan |
|
21 |
|
fvex |
|
22 |
|
sbcg |
|
23 |
21 22
|
ax-mp |
|
24 |
|
sbcel1v |
|
25 |
23 24
|
anbi12i |
|
26 |
20 25
|
bitri |
|
27 |
|
sbceq2g |
|
28 |
21 27
|
ax-mp |
|
29 |
26 28
|
anbi12i |
|
30 |
19 29
|
bitri |
|
31 |
30
|
sbcbii |
|
32 |
|
sbcan |
|
33 |
|
sbcan |
|
34 |
|
sbcel1v |
|
35 |
|
fvex |
|
36 |
|
sbcg |
|
37 |
35 36
|
ax-mp |
|
38 |
34 37
|
anbi12i |
|
39 |
33 38
|
bitri |
|
40 |
|
sbceq2g |
|
41 |
35 40
|
ax-mp |
|
42 |
39 41
|
anbi12i |
|
43 |
31 32 42
|
3bitri |
|
44 |
|
sbcan |
|
45 |
|
sbcg |
|
46 |
21 45
|
ax-mp |
|
47 |
|
sbcan |
|
48 |
|
sbcg |
|
49 |
21 48
|
ax-mp |
|
50 |
|
sbceq1g |
|
51 |
21 50
|
ax-mp |
|
52 |
21
|
csbvargi |
|
53 |
52
|
eqeq1i |
|
54 |
51 53
|
bitri |
|
55 |
49 54
|
anbi12i |
|
56 |
47 55
|
bitri |
|
57 |
46 56
|
anbi12i |
|
58 |
44 57
|
bitri |
|
59 |
58
|
sbcbii |
|
60 |
|
sbcan |
|
61 |
|
sbcg |
|
62 |
35 61
|
ax-mp |
|
63 |
|
sbcan |
|
64 |
|
sbceq1g |
|
65 |
35 64
|
ax-mp |
|
66 |
35
|
csbvargi |
|
67 |
66
|
eqeq1i |
|
68 |
65 67
|
bitri |
|
69 |
|
sbcg |
|
70 |
35 69
|
ax-mp |
|
71 |
68 70
|
anbi12i |
|
72 |
63 71
|
bitri |
|
73 |
62 72
|
anbi12i |
|
74 |
59 60 73
|
3bitri |
|
75 |
18 43 74
|
3bitr3g |
|
76 |
75
|
anbi2d |
|
77 |
16 76
|
syl5bb |
|
78 |
|
xpss |
|
79 |
|
simprr |
|
80 |
9
|
adantrr |
|
81 |
79 80
|
eqeltrd |
|
82 |
78 81
|
sseldi |
|
83 |
82
|
ex |
|
84 |
83
|
pm4.71rd |
|
85 |
|
eqop |
|
86 |
85
|
anbi2d |
|
87 |
86
|
pm5.32i |
|
88 |
84 87
|
bitr2di |
|
89 |
77 88
|
bitrd |
|
90 |
15 89
|
syl5bb |
|
91 |
90
|
opabbidv |
|
92 |
|
df-mpo |
|
93 |
1 92
|
eqtri |
|
94 |
93
|
cnveqi |
|
95 |
|
nfv |
|
96 |
|
nfv |
|
97 |
|
nfv |
|
98 |
|
nfcsb1v |
|
99 |
98
|
nfeq2 |
|
100 |
97 99
|
nfan |
|
101 |
|
nfv |
|
102 |
|
nfcv |
|
103 |
|
nfcsb1v |
|
104 |
102 103
|
nfcsbw |
|
105 |
104
|
nfeq2 |
|
106 |
101 105
|
nfan |
|
107 |
|
simpl |
|
108 |
107
|
eleq1d |
|
109 |
|
simpr |
|
110 |
109
|
eleq1d |
|
111 |
108 110
|
anbi12d |
|
112 |
|
csbeq1a |
|
113 |
|
csbeq1a |
|
114 |
112 113
|
sylan9eqr |
|
115 |
114
|
eqeq2d |
|
116 |
111 115
|
anbi12d |
|
117 |
95 96 100 106 116
|
cbvoprab12 |
|
118 |
117
|
cnveqi |
|
119 |
|
eleq1 |
|
120 |
|
opelxp |
|
121 |
119 120
|
syl6bb |
|
122 |
|
csbcom |
|
123 |
|
csbcow |
|
124 |
123
|
csbeq2i |
|
125 |
122 124
|
eqtri |
|
126 |
125
|
csbeq2i |
|
127 |
|
csbcow |
|
128 |
126 127
|
eqtri |
|
129 |
|
csbopeq1a |
|
130 |
128 129
|
syl5eqr |
|
131 |
130
|
eqeq2d |
|
132 |
121 131
|
anbi12d |
|
133 |
|
xpss |
|
134 |
133
|
sseli |
|
135 |
134
|
adantr |
|
136 |
132 135
|
cnvoprab |
|
137 |
94 118 136
|
3eqtri |
|
138 |
|
df-mpt |
|
139 |
91 137 138
|
3eqtr4g |
|
140 |
139
|
fneq1d |
|
141 |
13 140
|
mpbird |
|
142 |
|
dff1o4 |
|
143 |
7 141 142
|
sylanbrc |
|