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Mirrors > Home > MPE Home > Th. List > arwval | Structured version Visualization version Unicode version |
Description: The set of arrows is the union of all the disjointified hom-sets. (Contributed by Mario Carneiro, 11-Jan-2017.) |
Ref | Expression |
---|---|
arwval.a |
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arwval.h |
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Ref | Expression |
---|---|
arwval |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | arwval.a |
. 2
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2 | fveq2 5879 |
. . . . . . 7
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3 | arwval.h |
. . . . . . 7
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4 | 2, 3 | syl6eqr 2523 |
. . . . . 6
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5 | 4 | rneqd 5068 |
. . . . 5
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6 | 5 | unieqd 4200 |
. . . 4
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7 | df-arw 16000 |
. . . 4
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8 | fvex 5889 |
. . . . . . 7
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9 | 3, 8 | eqeltri 2545 |
. . . . . 6
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10 | 9 | rnex 6746 |
. . . . 5
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11 | 10 | uniex 6606 |
. . . 4
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12 | 6, 7, 11 | fvmpt 5963 |
. . 3
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13 | 7 | dmmptss 5338 |
. . . . . . 7
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14 | 13 | sseli 3414 |
. . . . . 6
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15 | 14 | con3i 142 |
. . . . 5
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16 | ndmfv 5903 |
. . . . 5
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17 | 15, 16 | syl 17 |
. . . 4
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18 | df-homa 15999 |
. . . . . . . . . . . . 13
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
19 | 18 | dmmptss 5338 |
. . . . . . . . . . . 12
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20 | 19 | sseli 3414 |
. . . . . . . . . . 11
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21 | 20 | con3i 142 |
. . . . . . . . . 10
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22 | ndmfv 5903 |
. . . . . . . . . 10
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23 | 21, 22 | syl 17 |
. . . . . . . . 9
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24 | 3, 23 | syl5eq 2517 |
. . . . . . . 8
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25 | 24 | rneqd 5068 |
. . . . . . 7
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26 | rn0 5092 |
. . . . . . 7
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27 | 25, 26 | syl6eq 2521 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
28 | 27 | unieqd 4200 |
. . . . 5
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29 | uni0 4217 |
. . . . 5
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30 | 28, 29 | syl6eq 2521 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
31 | 17, 30 | eqtr4d 2508 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
32 | 12, 31 | pm2.61i 169 |
. 2
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33 | 1, 32 | eqtri 2493 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-8 1906 ax-9 1913 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 ax-ext 2451 ax-sep 4518 ax-nul 4527 ax-pow 4579 ax-pr 4639 ax-un 6602 |
This theorem depends on definitions: df-bi 190 df-or 377 df-an 378 df-3an 1009 df-tru 1455 df-ex 1672 df-nf 1676 df-sb 1806 df-eu 2323 df-mo 2324 df-clab 2458 df-cleq 2464 df-clel 2467 df-nfc 2601 df-ne 2643 df-ral 2761 df-rex 2762 df-rab 2765 df-v 3033 df-sbc 3256 df-dif 3393 df-un 3395 df-in 3397 df-ss 3404 df-nul 3723 df-if 3873 df-sn 3960 df-pr 3962 df-op 3966 df-uni 4191 df-br 4396 df-opab 4455 df-mpt 4456 df-id 4754 df-xp 4845 df-rel 4846 df-cnv 4847 df-co 4848 df-dm 4849 df-rn 4850 df-res 4851 df-ima 4852 df-iota 5553 df-fun 5591 df-fv 5597 df-homa 15999 df-arw 16000 |
This theorem is referenced by: arwhoma 16018 homarw 16019 |
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