Step |
Hyp |
Ref |
Expression |
1 |
|
funcrngcsetcALT.r |
|
2 |
|
funcrngcsetcALT.s |
|
3 |
|
funcrngcsetcALT.b |
|
4 |
|
funcrngcsetcALT.u |
|
5 |
|
funcrngcsetcALT.f |
|
6 |
|
funcrngcsetcALT.g |
|
7 |
|
fveq2 |
|
8 |
7
|
cbvmptv |
|
9 |
5 8
|
eqtrdi |
|
10 |
|
coires1 |
|
11 |
1 3 4
|
rngcbas |
|
12 |
11
|
eleq2d |
|
13 |
|
elin |
|
14 |
13
|
simplbi |
|
15 |
12 14
|
syl6bi |
|
16 |
15
|
ssrdv |
|
17 |
16
|
resmptd |
|
18 |
10 17
|
syl5req |
|
19 |
9 18
|
eqtrd |
|
20 |
|
coires1 |
|
21 |
|
eqid |
|
22 |
|
eqid |
|
23 |
21 22
|
rnghmf |
|
24 |
|
fvex |
|
25 |
|
fvex |
|
26 |
24 25
|
pm3.2i |
|
27 |
|
elmapg |
|
28 |
26 27
|
mp1i |
|
29 |
23 28
|
syl5ibr |
|
30 |
29
|
ssrdv |
|
31 |
30
|
resabs1d |
|
32 |
20 31
|
syl5req |
|
33 |
32
|
mpoeq3dva |
|
34 |
6 33
|
eqtrd |
|
35 |
3
|
a1i |
|
36 |
3
|
a1i |
|
37 |
|
fvresi |
|
38 |
37
|
adantr |
|
39 |
38
|
adantl |
|
40 |
|
fvresi |
|
41 |
40
|
adantl |
|
42 |
41
|
adantl |
|
43 |
39 42
|
oveq12d |
|
44 |
|
eqidd |
|
45 |
|
simprr |
|
46 |
45
|
fveq2d |
|
47 |
|
simprl |
|
48 |
47
|
fveq2d |
|
49 |
46 48
|
oveq12d |
|
50 |
49
|
reseq2d |
|
51 |
15
|
com12 |
|
52 |
51
|
adantr |
|
53 |
52
|
impcom |
|
54 |
11
|
eleq2d |
|
55 |
|
elin |
|
56 |
55
|
simplbi |
|
57 |
54 56
|
syl6bi |
|
58 |
57
|
a1d |
|
59 |
58
|
imp32 |
|
60 |
|
ovex |
|
61 |
60
|
a1i |
|
62 |
61
|
resiexd |
|
63 |
44 50 53 59 62
|
ovmpod |
|
64 |
43 63
|
eqtr2d |
|
65 |
|
eqidd |
|
66 |
|
oveq12 |
|
67 |
66
|
reseq2d |
|
68 |
67
|
adantl |
|
69 |
|
simprl |
|
70 |
|
simprr |
|
71 |
|
ovex |
|
72 |
71
|
a1i |
|
73 |
72
|
resiexd |
|
74 |
65 68 69 70 73
|
ovmpod |
|
75 |
74
|
eqcomd |
|
76 |
64 75
|
coeq12d |
|
77 |
35 36 76
|
mpoeq123dva |
|
78 |
34 77
|
eqtrd |
|
79 |
19 78
|
opeq12d |
|
80 |
|
eqid |
|
81 |
|
eqid |
|
82 |
|
eqidd |
|
83 |
|
eqidd |
|
84 |
1 81 3 4 82 83
|
rngcifuestrc |
|
85 |
|
eqid |
|
86 |
|
eqid |
|
87 |
81 4
|
estrcbas |
|
88 |
87
|
mpteq1d |
|
89 |
|
fveq2 |
|
90 |
89
|
oveq2d |
|
91 |
90
|
reseq2d |
|
92 |
|
fveq2 |
|
93 |
92
|
oveq1d |
|
94 |
93
|
reseq2d |
|
95 |
91 94
|
cbvmpov |
|
96 |
95
|
a1i |
|
97 |
|
eqidd |
|
98 |
87 87 97
|
mpoeq123dv |
|
99 |
96 98
|
eqtrd |
|
100 |
81 2 85 86 4 88 99
|
funcestrcsetc |
|
101 |
80 84 100
|
cofuval2 |
|
102 |
79 101
|
eqtr4d |
|
103 |
|
df-br |
|
104 |
84 103
|
sylib |
|
105 |
|
df-br |
|
106 |
100 105
|
sylib |
|
107 |
104 106
|
cofucl |
|
108 |
102 107
|
eqeltrd |
|
109 |
|
df-br |
|
110 |
108 109
|
sylibr |
|