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Mirrors > Home > MPE Home > Th. List > dfid3 | Structured version Visualization version Unicode version |
Description: A stronger version of df-id 4768 that doesn't require ![]() ![]() |
Ref | Expression |
---|---|
dfid3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-id 4768 |
. 2
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2 | ancom 456 |
. . . . . . . . . . 11
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3 | equcom 1873 |
. . . . . . . . . . . 12
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4 | 3 | anbi1i 706 |
. . . . . . . . . . 11
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5 | 2, 4 | bitri 257 |
. . . . . . . . . 10
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6 | 5 | exbii 1729 |
. . . . . . . . 9
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7 | vex 3060 |
. . . . . . . . . 10
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8 | opeq2 4181 |
. . . . . . . . . . 11
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9 | 8 | eqeq2d 2472 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
10 | 7, 9 | ceqsexv 3096 |
. . . . . . . . 9
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11 | equid 1866 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() | |
12 | 11 | biantru 512 |
. . . . . . . . 9
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13 | 6, 10, 12 | 3bitri 279 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
14 | 13 | exbii 1729 |
. . . . . . 7
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15 | nfe1 1929 |
. . . . . . . 8
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16 | 15 | 19.9 1981 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
17 | 14, 16 | bitr4i 260 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
18 | opeq2 4181 |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
19 | 18 | eqeq2d 2472 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
20 | equequ2 1879 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
21 | 19, 20 | anbi12d 722 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
22 | 21 | sps 1954 |
. . . . . . . 8
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23 | 22 | drex1 2172 |
. . . . . . 7
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24 | 23 | drex2 2173 |
. . . . . 6
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25 | 17, 24 | syl5bb 265 |
. . . . 5
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26 | nfnae 2163 |
. . . . . 6
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27 | nfnae 2163 |
. . . . . . 7
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28 | nfcvd 2604 |
. . . . . . . . 9
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29 | nfcvf2 2627 |
. . . . . . . . . 10
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30 | nfcvd 2604 |
. . . . . . . . . 10
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31 | 29, 30 | nfopd 4197 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
32 | 28, 31 | nfeqd 2610 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
33 | 29, 30 | nfeqd 2610 |
. . . . . . . 8
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34 | 32, 33 | nfand 2019 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
35 | opeq2 4181 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
36 | 35 | eqeq2d 2472 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
37 | equequ2 1879 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
38 | 36, 37 | anbi12d 722 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
39 | 38 | a1i 11 |
. . . . . . 7
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40 | 27, 34, 39 | cbvexd 2130 |
. . . . . 6
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41 | 26, 40 | exbid 1975 |
. . . . 5
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42 | 25, 41 | pm2.61i 169 |
. . . 4
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43 | 42 | abbii 2578 |
. . 3
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44 | df-opab 4476 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
45 | df-opab 4476 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
46 | 43, 44, 45 | 3eqtr4i 2494 |
. 2
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47 | 1, 46 | eqtri 2484 |
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 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 993 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-rab 2758 df-v 3059 df-dif 3419 df-un 3421 df-in 3423 df-ss 3430 df-nul 3744 df-if 3894 df-sn 3981 df-pr 3983 df-op 3987 df-opab 4476 df-id 4768 |
This theorem is referenced by: dfid2 4771 reli 4981 opabresid 5177 ider 7423 cnmptid 20725 |
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