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Mirrors > Home > MPE Home > Th. List > ismir | Structured version Visualization version Unicode version |
Description: Property of the image by the point inversion function. Definition 7.5 of [Schwabhauser] p. 49. (Contributed by Thierry Arnoux, 3-Jun-2019.) |
Ref | Expression |
---|---|
mirval.p |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
mirval.d |
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mirval.i |
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mirval.l |
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mirval.s |
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mirval.g |
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mirval.a |
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mirfv.m |
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mirfv.b |
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ismir.1 |
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ismir.2 |
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ismir.3 |
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Ref | Expression |
---|---|
ismir |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mirval.p |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | mirval.d |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | mirval.i |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | mirval.l |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | mirval.s |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | mirval.g |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | mirval.a |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | mirfv.m |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9 | mirfv.b |
. . 3
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10 | 1, 2, 3, 4, 5, 6, 7, 8, 9 | mirfv 24694 |
. 2
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11 | ismir.2 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
12 | ismir.3 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
13 | ismir.1 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
14 | 1, 2, 3, 6, 9, 7 | mirreu3 24692 |
. . . 4
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15 | oveq2 6296 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
16 | 15 | eqeq1d 2452 |
. . . . . 6
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17 | oveq1 6295 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
18 | 17 | eleq2d 2513 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
19 | 16, 18 | anbi12d 716 |
. . . . 5
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20 | 19 | riota2 6272 |
. . . 4
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21 | 13, 14, 20 | syl2anc 666 |
. . 3
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22 | 11, 12, 21 | mpbi2and 931 |
. 2
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23 | 10, 22 | eqtr2d 2485 |
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 1668 ax-4 1681 ax-5 1757 ax-6 1804 ax-7 1850 ax-9 1895 ax-10 1914 ax-11 1919 ax-12 1932 ax-13 2090 ax-ext 2430 ax-rep 4514 ax-sep 4524 ax-nul 4533 ax-pr 4638 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 986 df-tru 1446 df-ex 1663 df-nf 1667 df-sb 1797 df-eu 2302 df-mo 2303 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2580 df-ne 2623 df-ral 2741 df-rex 2742 df-reu 2743 df-rmo 2744 df-rab 2745 df-v 3046 df-sbc 3267 df-csb 3363 df-dif 3406 df-un 3408 df-in 3410 df-ss 3417 df-nul 3731 df-if 3881 df-pw 3952 df-sn 3968 df-pr 3970 df-op 3974 df-uni 4198 df-iun 4279 df-br 4402 df-opab 4461 df-mpt 4462 df-id 4748 df-xp 4839 df-rel 4840 df-cnv 4841 df-co 4842 df-dm 4843 df-rn 4844 df-res 4845 df-ima 4846 df-iota 5545 df-fun 5583 df-fn 5584 df-f 5585 df-f1 5586 df-fo 5587 df-f1o 5588 df-fv 5589 df-riota 6250 df-ov 6291 df-trkgc 24489 df-trkgb 24490 df-trkgcb 24491 df-trkg 24494 df-mir 24691 |
This theorem is referenced by: mirmir 24700 mireq 24703 mirinv 24704 miriso 24708 mirmir2 24712 mirauto 24722 colmid 24726 krippenlem 24728 midexlem 24730 mideulem2 24769 opphllem 24770 midcom 24817 trgcopyeulem 24840 |
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