Step | Hyp | Ref
| Expression |
1 | | ringccatidALTV.b |
. . 3
|
2 | 1 | a1i 11 |
. 2
|
3 | | eqidd 2623 |
. 2
|
4 | | eqidd 2623 |
. 2
comp comp |
5 | | ringccatALTV.c |
. . . 4
RingCatALTV |
6 | | fvex 6201 |
. . . 4
RingCatALTV |
7 | 5, 6 | eqeltri 2697 |
. . 3
|
8 | 7 | a1i 11 |
. 2
|
9 | | biid 251 |
. 2
|
10 | | simpl 473 |
. . . . . 6
|
11 | 5, 1, 10 | ringcbasALTV 42046 |
. . . . 5
|
12 | | eleq2 2690 |
. . . . . . . 8
|
13 | | elin 3796 |
. . . . . . . . 9
|
14 | 13 | simprbi 480 |
. . . . . . . 8
|
15 | 12, 14 | syl6bi 243 |
. . . . . . 7
|
16 | 15 | com12 32 |
. . . . . 6
|
17 | 16 | adantl 482 |
. . . . 5
|
18 | 11, 17 | mpd 15 |
. . . 4
|
19 | | eqid 2622 |
. . . . 5
|
20 | 19 | idrhm 18731 |
. . . 4
RingHom |
21 | 18, 20 | syl 17 |
. . 3
RingHom |
22 | | eqid 2622 |
. . . 4
|
23 | | simpr 477 |
. . . 4
|
24 | 5, 1, 10, 22, 23, 23 | ringchomALTV 42048 |
. . 3
RingHom |
25 | 21, 24 | eleqtrrd 2704 |
. 2
|
26 | | simpl 473 |
. . . 4
|
27 | | eqid 2622 |
. . . 4
comp comp |
28 | | simpl 473 |
. . . . . 6
|
29 | 28 | 3ad2ant1 1082 |
. . . . 5
|
30 | 29 | adantl 482 |
. . . 4
|
31 | | simpr 477 |
. . . . . 6
|
32 | 31 | 3ad2ant1 1082 |
. . . . 5
|
33 | 32 | adantl 482 |
. . . 4
|
34 | | simp1 1061 |
. . . . . . . . . . . . 13
|
35 | 28 | 3ad2ant3 1084 |
. . . . . . . . . . . . 13
|
36 | 31 | 3ad2ant3 1084 |
. . . . . . . . . . . . 13
|
37 | 5, 1, 34, 22, 35, 36 | ringchomALTV 42048 |
. . . . . . . . . . . 12
RingHom |
38 | 37 | eleq2d 2687 |
. . . . . . . . . . 11
RingHom |
39 | 38 | biimpd 219 |
. . . . . . . . . 10
RingHom |
40 | 39 | 3exp 1264 |
. . . . . . . . 9
RingHom |
41 | 40 | com14 96 |
. . . . . . . 8
RingHom |
42 | 41 | 3ad2ant1 1082 |
. . . . . . 7
RingHom |
43 | 42 | com13 88 |
. . . . . 6
RingHom |
44 | 43 | 3imp 1256 |
. . . . 5
RingHom |
45 | 44 | impcom 446 |
. . . 4
RingHom |
46 | 21 | expcom 451 |
. . . . . . 7
RingHom |
47 | 46 | adantl 482 |
. . . . . 6
RingHom |
48 | 47 | 3ad2ant1 1082 |
. . . . 5
RingHom |
49 | 48 | impcom 446 |
. . . 4
RingHom |
50 | 5, 1, 26, 27, 30, 33, 33, 45, 49 | ringccoALTV 42051 |
. . 3
comp |
51 | | simpl 473 |
. . . . . . . . . . . 12
|
52 | | simprl 794 |
. . . . . . . . . . . 12
|
53 | | simprr 796 |
. . . . . . . . . . . 12
|
54 | 5, 1, 51, 22, 52, 53 | elringchomALTV 42049 |
. . . . . . . . . . 11
|
55 | 54 | ex 450 |
. . . . . . . . . 10
|
56 | 55 | com13 88 |
. . . . . . . . 9
|
57 | | fcoi2 6079 |
. . . . . . . . 9
|
58 | 56, 57 | syl8 76 |
. . . . . . . 8
|
59 | 58 | 3ad2ant1 1082 |
. . . . . . 7
|
60 | 59 | com12 32 |
. . . . . 6
|
61 | 60 | a1d 25 |
. . . . 5
|
62 | 61 | 3imp 1256 |
. . . 4
|
63 | 62 | impcom 446 |
. . 3
|
64 | 50, 63 | eqtrd 2656 |
. 2
comp |
65 | | simp3 1063 |
. . . . . . . . 9
|
66 | 31 | adantr 481 |
. . . . . . . . . 10
|
67 | 66 | 3ad2ant2 1083 |
. . . . . . . . 9
|
68 | | simprl 794 |
. . . . . . . . . 10
|
69 | 68 | 3ad2ant2 1083 |
. . . . . . . . 9
|
70 | 47 | adantr 481 |
. . . . . . . . . . 11
RingHom |
71 | 70 | a1i 11 |
. . . . . . . . . 10
RingHom |
72 | 71 | 3imp 1256 |
. . . . . . . . 9
RingHom |
73 | | simpl 473 |
. . . . . . . . . . . . . . 15
|
74 | 66 | adantl 482 |
. . . . . . . . . . . . . . 15
|
75 | 68 | adantl 482 |
. . . . . . . . . . . . . . 15
|
76 | 5, 1, 73, 22, 74, 75 | ringchomALTV 42048 |
. . . . . . . . . . . . . 14
RingHom |
77 | 76 | eleq2d 2687 |
. . . . . . . . . . . . 13
RingHom |
78 | 77 | biimpd 219 |
. . . . . . . . . . . 12
RingHom |
79 | 78 | ex 450 |
. . . . . . . . . . 11
RingHom |
80 | 79 | com13 88 |
. . . . . . . . . 10
RingHom |
81 | 80 | 3imp 1256 |
. . . . . . . . 9
RingHom |
82 | 5, 1, 65, 27, 67, 67, 69, 72, 81 | ringccoALTV 42051 |
. . . . . . . 8
comp
|
83 | 5, 1, 73, 22, 74, 75 | elringchomALTV 42049 |
. . . . . . . . . . . 12
|
84 | 83 | ex 450 |
. . . . . . . . . . 11
|
85 | 84 | com13 88 |
. . . . . . . . . 10
|
86 | 85 | 3imp 1256 |
. . . . . . . . 9
|
87 | | fcoi1 6078 |
. . . . . . . . 9
|
88 | 86, 87 | syl 17 |
. . . . . . . 8
|
89 | 82, 88 | eqtrd 2656 |
. . . . . . 7
comp
|
90 | 89 | 3exp 1264 |
. . . . . 6
comp |
91 | 90 | 3ad2ant2 1083 |
. . . . 5
comp |
92 | 91 | expdcom 455 |
. . . 4
comp |
93 | 92 | 3imp 1256 |
. . 3
comp
|
94 | 93 | impcom 446 |
. 2
comp |
95 | | simpl 473 |
. . . . . . . . . . . . . 14
|
96 | 95 | 3ad2ant2 1083 |
. . . . . . . . . . . . 13
|
97 | 5, 1, 34, 22, 36, 96 | ringchomALTV 42048 |
. . . . . . . . . . . 12
RingHom |
98 | 97 | eleq2d 2687 |
. . . . . . . . . . 11
RingHom |
99 | 98 | biimpd 219 |
. . . . . . . . . 10
RingHom |
100 | 99 | 3exp 1264 |
. . . . . . . . 9
RingHom |
101 | 100 | com14 96 |
. . . . . . . 8
RingHom |
102 | 101 | 3ad2ant2 1083 |
. . . . . . 7
RingHom |
103 | 102 | com13 88 |
. . . . . 6
RingHom |
104 | 103 | 3imp 1256 |
. . . . 5
RingHom |
105 | 104 | impcom 446 |
. . . 4
RingHom |
106 | | rhmco 18737 |
. . . 4
RingHom RingHom
RingHom |
107 | 105, 45, 106 | syl2anc 693 |
. . 3
RingHom |
108 | 95 | 3ad2ant2 1083 |
. . . . 5
|
109 | 108 | adantl 482 |
. . . 4
|
110 | 5, 1, 26, 27, 30, 33, 109, 45, 105 | ringccoALTV 42051 |
. . 3
comp |
111 | 5, 1, 26, 22, 30, 109 | ringchomALTV 42048 |
. . 3
RingHom |
112 | 107, 110,
111 | 3eltr4d 2716 |
. 2
comp |
113 | | coass 5654 |
. . . 4
|
114 | | simp2r 1088 |
. . . . . 6
|
115 | 114 | adantl 482 |
. . . . 5
|
116 | | simp2r 1088 |
. . . . . . . . . . . . . . 15
|
117 | 5, 1, 34, 22, 96, 116 | ringchomALTV 42048 |
. . . . . . . . . . . . . 14
RingHom |
118 | 117 | eleq2d 2687 |
. . . . . . . . . . . . 13
RingHom |
119 | 118 | biimpd 219 |
. . . . . . . . . . . 12
RingHom |
120 | 119 | 3exp 1264 |
. . . . . . . . . . 11
RingHom |
121 | 120 | com14 96 |
. . . . . . . . . 10
RingHom |
122 | 121 | 3ad2ant3 1084 |
. . . . . . . . 9
RingHom |
123 | 122 | com13 88 |
. . . . . . . 8
RingHom |
124 | 123 | 3imp 1256 |
. . . . . . 7
RingHom |
125 | 124 | impcom 446 |
. . . . . 6
RingHom |
126 | | rhmco 18737 |
. . . . . 6
RingHom RingHom
RingHom |
127 | 125, 105,
126 | syl2anc 693 |
. . . . 5
RingHom |
128 | 5, 1, 26, 27, 30, 33, 115, 45, 127 | ringccoALTV 42051 |
. . . 4
comp |
129 | 5, 1, 26, 27, 30, 109, 115, 107, 125 | ringccoALTV 42051 |
. . . 4
comp |
130 | 113, 128,
129 | 3eqtr4a 2682 |
. . 3
comp comp |
131 | 5, 1, 26, 27, 33, 109, 115, 105, 125 | ringccoALTV 42051 |
. . . 4
comp |
132 | 131 | oveq1d 6665 |
. . 3
comp comp comp |
133 | 110 | oveq2d 6666 |
. . 3
comp comp comp |
134 | 130, 132,
133 | 3eqtr4d 2666 |
. 2
comp comp comp comp |
135 | 2, 3, 4, 8, 9, 25,
64, 94, 112, 134 | iscatd2 16342 |
1
|