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Mathbox for Scott Fenton |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > dfiota3 | Structured version Visualization version Unicode version |
Description: A definiton of iota using minimal quantifiers. (Contributed by Scott Fenton, 19-Feb-2013.) |
Ref | Expression |
---|---|
dfiota3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-iota 5553 |
. 2
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2 | abeq1 2581 |
. . . . 5
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3 | exdistr 1843 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | vex 3034 |
. . . . . . . . 9
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5 | sneq 3969 |
. . . . . . . . . 10
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6 | 5 | eqeq2d 2481 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7 | 4, 6 | ceqsexv 3070 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
8 | snex 4641 |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() ![]() ![]() | |
9 | eqeq1 2475 |
. . . . . . . . . . . . 13
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
10 | eleq2 2538 |
. . . . . . . . . . . . 13
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
11 | 9, 10 | anbi12d 725 |
. . . . . . . . . . . 12
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12 | eqcom 2478 |
. . . . . . . . . . . . 13
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
13 | elsn 3973 |
. . . . . . . . . . . . . 14
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
14 | equcom 1870 |
. . . . . . . . . . . . . 14
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
15 | 13, 14 | bitri 257 |
. . . . . . . . . . . . 13
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
16 | 12, 15 | anbi12ci 712 |
. . . . . . . . . . . 12
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
17 | 11, 16 | syl6bb 269 |
. . . . . . . . . . 11
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18 | 8, 17 | ceqsexv 3070 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
19 | an13 816 |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
20 | 19 | exbii 1726 |
. . . . . . . . . 10
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21 | 18, 20 | bitr3i 259 |
. . . . . . . . 9
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22 | 21 | exbii 1726 |
. . . . . . . 8
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23 | 7, 22 | bitr3i 259 |
. . . . . . 7
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24 | excom 1944 |
. . . . . . 7
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25 | 23, 24 | bitri 257 |
. . . . . 6
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26 | eluniab 4201 |
. . . . . 6
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27 | 3, 25, 26 | 3bitr4i 285 |
. . . . 5
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28 | 2, 27 | mpgbir 1681 |
. . . 4
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29 | df-sn 3960 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
30 | dfsingles2 30759 |
. . . . . . 7
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31 | 29, 30 | ineq12i 3623 |
. . . . . 6
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32 | inab 3702 |
. . . . . . 7
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33 | 19.42v 1842 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
34 | 33 | bicomi 207 |
. . . . . . . 8
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35 | 34 | abbii 2587 |
. . . . . . 7
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36 | 32, 35 | eqtri 2493 |
. . . . . 6
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37 | 31, 36 | eqtri 2493 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
38 | 37 | unieqi 4199 |
. . . 4
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39 | 28, 38 | eqtr4i 2496 |
. . 3
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40 | 39 | unieqi 4199 |
. 2
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41 | 1, 40 | 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-symdif 3654 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-eprel 4750 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-iota 5553 df-fun 5591 df-fn 5592 df-f 5593 df-fo 5595 df-fv 5597 df-1st 6812 df-2nd 6813 df-txp 30691 df-singleton 30699 df-singles 30700 |
This theorem is referenced by: dffv5 30762 |
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