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Mirrors > Home > MPE Home > Th. List > issect | Structured version Visualization version Unicode version |
Description: The property "![]() ![]() |
Ref | Expression |
---|---|
issect.b |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
issect.h |
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issect.o |
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issect.i |
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issect.s |
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issect.c |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
issect.x |
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issect.y |
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Ref | Expression |
---|---|
issect |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | issect.b |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | issect.h |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | issect.o |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | issect.i |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | issect.s |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | issect.c |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | issect.x |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | issect.y |
. . . 4
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9 | 1, 2, 3, 4, 5, 6, 7, 8 | sectfval 15734 |
. . 3
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10 | 9 | breqd 4406 |
. 2
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11 | oveq12 6317 |
. . . . . 6
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12 | 11 | ancoms 460 |
. . . . 5
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13 | 12 | eqeq1d 2473 |
. . . 4
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14 | eqid 2471 |
. . . 4
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15 | 13, 14 | brab2a 4889 |
. . 3
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16 | df-3an 1009 |
. . 3
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17 | 15, 16 | bitr4i 260 |
. 2
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18 | 10, 17 | syl6bb 269 |
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-rep 4508 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-reu 2763 df-rab 2765 df-v 3033 df-sbc 3256 df-csb 3350 df-dif 3393 df-un 3395 df-in 3397 df-ss 3404 df-nul 3723 df-if 3873 df-pw 3944 df-sn 3960 df-pr 3962 df-op 3966 df-uni 4191 df-iun 4271 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-fn 5592 df-f 5593 df-f1 5594 df-fo 5595 df-f1o 5596 df-fv 5597 df-ov 6311 df-oprab 6312 df-mpt2 6313 df-1st 6812 df-2nd 6813 df-sect 15730 |
This theorem is referenced by: issect2 15737 sectcan 15738 sectco 15739 oppcsect 15761 sectmon 15765 monsect 15766 funcsect 15855 fucsect 15955 invfuc 15957 setcsect 16062 catciso 16080 rngcsect 40490 rngcsectALTV 40502 ringcsect 40541 ringcsectALTV 40565 |
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