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Mirrors > Home > ILE Home > Th. List > df-mhm | Unicode version |
Description: A monoid homomorphism is a function on the base sets which preserves the binary operation and the identity. (Contributed by Mario Carneiro, 7-Mar-2015.) |
Ref | Expression |
---|---|
df-mhm |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cmhm 12736 |
. 2
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2 | vs |
. . 3
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3 | vt |
. . 3
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4 | cmnd 12706 |
. . 3
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5 | vx |
. . . . . . . . . . 11
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6 | 5 | cv 1352 |
. . . . . . . . . 10
![]() ![]() |
7 | vy |
. . . . . . . . . . 11
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8 | 7 | cv 1352 |
. . . . . . . . . 10
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9 | 2 | cv 1352 |
. . . . . . . . . . 11
![]() ![]() |
10 | cplusg 12515 |
. . . . . . . . . . 11
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11 | 9, 10 | cfv 5212 |
. . . . . . . . . 10
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12 | 6, 8, 11 | co 5869 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
13 | vf |
. . . . . . . . . 10
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14 | 13 | cv 1352 |
. . . . . . . . 9
![]() ![]() |
15 | 12, 14 | cfv 5212 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
16 | 6, 14 | cfv 5212 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() |
17 | 8, 14 | cfv 5212 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() |
18 | 3 | cv 1352 |
. . . . . . . . . 10
![]() ![]() |
19 | 18, 10 | cfv 5212 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() |
20 | 16, 17, 19 | co 5869 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
21 | 15, 20 | wceq 1353 |
. . . . . . 7
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22 | cbs 12442 |
. . . . . . . 8
![]() ![]() | |
23 | 9, 22 | cfv 5212 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() |
24 | 21, 7, 23 | wral 2455 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
25 | 24, 5, 23 | wral 2455 |
. . . . 5
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26 | c0g 12650 |
. . . . . . . 8
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27 | 9, 26 | cfv 5212 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() |
28 | 27, 14 | cfv 5212 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
29 | 18, 26 | cfv 5212 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() |
30 | 28, 29 | wceq 1353 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
31 | 25, 30 | wa 104 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
32 | 18, 22 | cfv 5212 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() |
33 | cmap 6642 |
. . . . 5
![]() ![]() | |
34 | 32, 23, 33 | co 5869 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
35 | 31, 13, 34 | crab 2459 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
36 | 2, 3, 4, 4, 35 | cmpo 5871 |
. 2
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37 | 1, 36 | wceq 1353 |
1
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Colors of variables: wff set class |
This definition is referenced by: ismhm 12740 mhmrcl1 12741 mhmrcl2 12742 |
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