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Mirrors > Home > MPE Home > Th. List > Mathboxes > setinds | Structured version Visualization version Unicode version |
Description: Principle of ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
setinds.1 |
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Ref | Expression |
---|---|
setinds |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 3034 |
. 2
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2 | setind 8236 |
. . . . 5
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3 | dfss3 3408 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | df-sbc 3256 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 4 | ralbii 2823 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6 | nfcv 2612 |
. . . . . . . . . . 11
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7 | nfsbc1v 3275 |
. . . . . . . . . . 11
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8 | 6, 7 | nfral 2789 |
. . . . . . . . . 10
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9 | nfsbc1v 3275 |
. . . . . . . . . 10
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10 | 8, 9 | nfim 2023 |
. . . . . . . . 9
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11 | raleq 2973 |
. . . . . . . . . 10
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12 | sbceq1a 3266 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
13 | 11, 12 | imbi12d 327 |
. . . . . . . . 9
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14 | setinds.1 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
15 | 10, 13, 14 | chvar 2119 |
. . . . . . . 8
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16 | 5, 15 | sylbir 218 |
. . . . . . 7
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17 | 3, 16 | sylbi 200 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
18 | df-sbc 3256 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
19 | 17, 18 | sylib 201 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
20 | 2, 19 | mpg 1679 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
21 | 20 | eqcomi 2480 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
22 | 21 | abeq2i 2583 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | 1, 22 | mpbi 213 |
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 ax-reg 8125 ax-inf2 8164 |
This theorem depends on definitions: df-bi 190 df-or 377 df-an 378 df-3or 1008 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-pss 3406 df-nul 3723 df-if 3873 df-pw 3944 df-sn 3960 df-pr 3962 df-tp 3964 df-op 3966 df-uni 4191 df-iun 4271 df-br 4396 df-opab 4455 df-mpt 4456 df-tr 4491 df-eprel 4750 df-id 4754 df-po 4760 df-so 4761 df-fr 4798 df-we 4800 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-pred 5387 df-ord 5433 df-on 5434 df-lim 5435 df-suc 5436 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-om 6712 df-wrecs 7046 df-recs 7108 df-rdg 7146 |
This theorem is referenced by: setinds2f 30496 |
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