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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 5870 |
. . . . . . 7
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3 | arwval.h |
. . . . . . 7
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4 | 2, 3 | syl6eqr 2505 |
. . . . . 6
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5 | 4 | rneqd 5065 |
. . . . 5
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6 | 5 | unieqd 4211 |
. . . 4
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7 | df-arw 15934 |
. . . 4
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8 | fvex 5880 |
. . . . . . 7
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9 | 3, 8 | eqeltri 2527 |
. . . . . 6
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10 | 9 | rnex 6732 |
. . . . 5
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11 | 10 | uniex 6592 |
. . . 4
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12 | 6, 7, 11 | fvmpt 5953 |
. . 3
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13 | 7 | dmmptss 5334 |
. . . . . . 7
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14 | 13 | sseli 3430 |
. . . . . 6
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15 | 14 | con3i 141 |
. . . . 5
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16 | ndmfv 5894 |
. . . . 5
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17 | 15, 16 | syl 17 |
. . . 4
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18 | df-homa 15933 |
. . . . . . . . . . . . 13
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
19 | 18 | dmmptss 5334 |
. . . . . . . . . . . 12
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20 | 19 | sseli 3430 |
. . . . . . . . . . 11
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21 | 20 | con3i 141 |
. . . . . . . . . 10
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22 | ndmfv 5894 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
23 | 21, 22 | syl 17 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 3, 23 | syl5eq 2499 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
25 | 24 | rneqd 5065 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
26 | rn0 5089 |
. . . . . . 7
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27 | 25, 26 | syl6eq 2503 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
28 | 27 | unieqd 4211 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
29 | uni0 4228 |
. . . . 5
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30 | 28, 29 | syl6eq 2503 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
31 | 17, 30 | eqtr4d 2490 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
32 | 12, 31 | pm2.61i 168 |
. 2
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33 | 1, 32 | eqtri 2475 |
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 1671 ax-4 1684 ax-5 1760 ax-6 1807 ax-7 1853 ax-8 1891 ax-9 1898 ax-10 1917 ax-11 1922 ax-12 1935 ax-13 2093 ax-ext 2433 ax-sep 4528 ax-nul 4537 ax-pow 4584 ax-pr 4642 ax-un 6588 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 988 df-tru 1449 df-ex 1666 df-nf 1670 df-sb 1800 df-eu 2305 df-mo 2306 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2583 df-ne 2626 df-ral 2744 df-rex 2745 df-rab 2748 df-v 3049 df-sbc 3270 df-dif 3409 df-un 3411 df-in 3413 df-ss 3420 df-nul 3734 df-if 3884 df-sn 3971 df-pr 3973 df-op 3977 df-uni 4202 df-br 4406 df-opab 4465 df-mpt 4466 df-id 4752 df-xp 4843 df-rel 4844 df-cnv 4845 df-co 4846 df-dm 4847 df-rn 4848 df-res 4849 df-ima 4850 df-iota 5549 df-fun 5587 df-fv 5593 df-homa 15933 df-arw 15934 |
This theorem is referenced by: arwhoma 15952 homarw 15953 |
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