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Mirrors > Home > ILE Home > Th. List > df-pt | Unicode version |
Description: Define the product topology on a collection of topologies. For convenience, it is defined on arbitrary collections of sets, expressed as a function from some index set to the subbases of each factor space. (Contributed by Mario Carneiro, 3-Feb-2015.) |
Ref | Expression |
---|---|
df-pt |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cpt 12704 |
. 2
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2 | vf |
. . 3
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3 | cvv 2738 |
. . 3
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4 | vg |
. . . . . . . . . 10
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5 | 4 | cv 1352 |
. . . . . . . . 9
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6 | 2 | cv 1352 |
. . . . . . . . . 10
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7 | 6 | cdm 4627 |
. . . . . . . . 9
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8 | 5, 7 | wfn 5212 |
. . . . . . . 8
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9 | vy |
. . . . . . . . . . . 12
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10 | 9 | cv 1352 |
. . . . . . . . . . 11
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11 | 10, 5 | cfv 5217 |
. . . . . . . . . 10
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12 | 10, 6 | cfv 5217 |
. . . . . . . . . 10
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13 | 11, 12 | wcel 2148 |
. . . . . . . . 9
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14 | 13, 9, 7 | wral 2455 |
. . . . . . . 8
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15 | 12 | cuni 3810 |
. . . . . . . . . . 11
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16 | 11, 15 | wceq 1353 |
. . . . . . . . . 10
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17 | vz |
. . . . . . . . . . . 12
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18 | 17 | cv 1352 |
. . . . . . . . . . 11
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19 | 7, 18 | cdif 3127 |
. . . . . . . . . 10
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20 | 16, 9, 19 | wral 2455 |
. . . . . . . . 9
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21 | cfn 6740 |
. . . . . . . . 9
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22 | 20, 17, 21 | wrex 2456 |
. . . . . . . 8
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23 | 8, 14, 22 | w3a 978 |
. . . . . . 7
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24 | vx |
. . . . . . . . 9
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25 | 24 | cv 1352 |
. . . . . . . 8
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26 | 9, 7, 11 | cixp 6698 |
. . . . . . . 8
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27 | 25, 26 | wceq 1353 |
. . . . . . 7
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28 | 23, 27 | wa 104 |
. . . . . 6
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29 | 28, 4 | wex 1492 |
. . . . 5
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30 | 29, 24 | cab 2163 |
. . . 4
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31 | ctg 12703 |
. . . 4
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32 | 30, 31 | cfv 5217 |
. . 3
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33 | 2, 3, 32 | cmpt 4065 |
. 2
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34 | 1, 33 | wceq 1353 |
1
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Colors of variables: wff set class |
This definition is referenced by: ptex 12713 |
Copyright terms: Public domain | W3C validator |