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Mirrors > Home > MPE Home > Th. List > df-om1 | Unicode version |
Description: Define the loop space of a topological space, with a magma structure on it given by concatenation of loops. This structure is not a group, but the operation is compatible with homotopy, which allows the homotopy groups to be defined based on this operation. (Contributed by Mario Carneiro, 10-Jul-2015.) |
Ref | Expression |
---|---|
df-om1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | comi 18979 |
. 2
![]() ![]() ![]() | |
2 | vj |
. . 3
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3 | vy |
. . 3
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4 | ctop 16913 |
. . 3
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5 | 2 | cv 1648 |
. . . 4
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6 | 5 | cuni 3975 |
. . 3
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7 | cnx 13421 |
. . . . . 6
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8 | cbs 13424 |
. . . . . 6
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9 | 7, 8 | cfv 5413 |
. . . . 5
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10 | cc0 8946 |
. . . . . . . . 9
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11 | vf |
. . . . . . . . . 10
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12 | 11 | cv 1648 |
. . . . . . . . 9
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13 | 10, 12 | cfv 5413 |
. . . . . . . 8
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14 | 3 | cv 1648 |
. . . . . . . 8
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15 | 13, 14 | wceq 1649 |
. . . . . . 7
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16 | c1 8947 |
. . . . . . . . 9
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17 | 16, 12 | cfv 5413 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() |
18 | 17, 14 | wceq 1649 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
19 | 15, 18 | wa 359 |
. . . . . 6
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20 | cii 18858 |
. . . . . . 7
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21 | ccn 17242 |
. . . . . . 7
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22 | 20, 5, 21 | co 6040 |
. . . . . 6
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23 | 19, 11, 22 | crab 2670 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 9, 23 | cop 3777 |
. . . 4
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25 | cplusg 13484 |
. . . . . 6
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26 | 7, 25 | cfv 5413 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() |
27 | cpco 18978 |
. . . . . 6
![]() ![]() | |
28 | 5, 27 | cfv 5413 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() |
29 | 26, 28 | cop 3777 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
30 | cts 13490 |
. . . . . 6
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31 | 7, 30 | cfv 5413 |
. . . . 5
![]() ![]() ![]() ![]() ![]() |
32 | cxko 17546 |
. . . . . 6
![]() ![]() ![]() ![]() | |
33 | 5, 20, 32 | co 6040 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
34 | 31, 33 | cop 3777 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
35 | 24, 29, 34 | ctp 3776 |
. . 3
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36 | 2, 3, 4, 6, 35 | cmpt2 6042 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
37 | 1, 36 | wceq 1649 |
1
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Colors of variables: wff set class |
This definition is referenced by: om1val 19008 |
Copyright terms: Public domain | W3C validator |