Step |
Hyp |
Ref |
Expression |
1 |
|
bren |
|
2 |
|
bren |
|
3 |
|
exdistrv |
|
4 |
|
f1of |
|
5 |
|
f1odm |
|
6 |
|
vex |
|
7 |
6
|
dmex |
|
8 |
5 7
|
eqeltrrdi |
|
9 |
|
f1odm |
|
10 |
|
vex |
|
11 |
10
|
dmex |
|
12 |
9 11
|
eqeltrrdi |
|
13 |
|
elmapg |
|
14 |
8 12 13
|
syl2anr |
|
15 |
4 14
|
syl5ibr |
|
16 |
15
|
abssdv |
|
17 |
|
ovex |
|
18 |
17
|
ssex |
|
19 |
16 18
|
syl |
|
20 |
|
f1of |
|
21 |
|
f1ofo |
|
22 |
|
forn |
|
23 |
21 22
|
syl |
|
24 |
6
|
rnex |
|
25 |
23 24
|
eqeltrrdi |
|
26 |
|
f1ofo |
|
27 |
|
forn |
|
28 |
26 27
|
syl |
|
29 |
10
|
rnex |
|
30 |
28 29
|
eqeltrrdi |
|
31 |
|
elmapg |
|
32 |
25 30 31
|
syl2anr |
|
33 |
20 32
|
syl5ibr |
|
34 |
33
|
abssdv |
|
35 |
|
ovex |
|
36 |
35
|
ssex |
|
37 |
34 36
|
syl |
|
38 |
|
f1oco |
|
39 |
38
|
adantll |
|
40 |
|
f1ocnv |
|
41 |
40
|
ad2antrr |
|
42 |
|
f1oco |
|
43 |
39 41 42
|
syl2anc |
|
44 |
43
|
ex |
|
45 |
|
vex |
|
46 |
|
f1oeq1 |
|
47 |
45 46
|
elab |
|
48 |
6 45
|
coex |
|
49 |
10
|
cnvex |
|
50 |
48 49
|
coex |
|
51 |
|
f1oeq1 |
|
52 |
50 51
|
elab |
|
53 |
44 47 52
|
3imtr4g |
|
54 |
|
f1ocnv |
|
55 |
54
|
ad2antlr |
|
56 |
|
f1oco |
|
57 |
56
|
ancoms |
|
58 |
57
|
adantlr |
|
59 |
|
f1oco |
|
60 |
55 58 59
|
syl2anc |
|
61 |
60
|
ex |
|
62 |
|
vex |
|
63 |
|
f1oeq1 |
|
64 |
62 63
|
elab |
|
65 |
6
|
cnvex |
|
66 |
62 10
|
coex |
|
67 |
65 66
|
coex |
|
68 |
|
f1oeq1 |
|
69 |
67 68
|
elab |
|
70 |
61 64 69
|
3imtr4g |
|
71 |
47 64
|
anbi12i |
|
72 |
|
coass |
|
73 |
|
f1ococnv1 |
|
74 |
73
|
ad2antrr |
|
75 |
74
|
coeq2d |
|
76 |
39
|
adantrr |
|
77 |
|
f1of |
|
78 |
|
fcoi1 |
|
79 |
76 77 78
|
3syl |
|
80 |
75 79
|
eqtrd |
|
81 |
72 80
|
eqtr2id |
|
82 |
|
coass |
|
83 |
|
f1ococnv2 |
|
84 |
83
|
ad2antlr |
|
85 |
84
|
coeq1d |
|
86 |
58
|
adantrl |
|
87 |
|
f1of |
|
88 |
|
fcoi2 |
|
89 |
86 87 88
|
3syl |
|
90 |
85 89
|
eqtrd |
|
91 |
82 90
|
eqtr3id |
|
92 |
81 91
|
eqeq12d |
|
93 |
|
eqcom |
|
94 |
92 93
|
bitrdi |
|
95 |
|
f1of1 |
|
96 |
95
|
ad2antlr |
|
97 |
|
f1of |
|
98 |
97
|
ad2antrl |
|
99 |
60
|
adantrl |
|
100 |
|
f1of |
|
101 |
99 100
|
syl |
|
102 |
|
cocan1 |
|
103 |
96 98 101 102
|
syl3anc |
|
104 |
26
|
ad2antrr |
|
105 |
|
f1ofn |
|
106 |
105
|
ad2antll |
|
107 |
43
|
adantrr |
|
108 |
|
f1ofn |
|
109 |
107 108
|
syl |
|
110 |
|
cocan2 |
|
111 |
104 106 109 110
|
syl3anc |
|
112 |
94 103 111
|
3bitr3d |
|
113 |
112
|
ex |
|
114 |
71 113
|
syl5bi |
|
115 |
19 37 53 70 114
|
en3d |
|
116 |
115
|
exlimivv |
|
117 |
3 116
|
sylbir |
|
118 |
1 2 117
|
syl2anb |
|