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Mirrors > Home > ILE Home > Th. List > imadiflem | Unicode version |
Description: One direction of imadif 5211. This direction does not require
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Ref | Expression |
---|---|
imadiflem |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2423 |
. . . 4
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2 | df-rex 2423 |
. . . . 5
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3 | 2 | notbii 658 |
. . . 4
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4 | alnex 1476 |
. . . . . . 7
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5 | 19.29r 1601 |
. . . . . . 7
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6 | 4, 5 | sylan2br 286 |
. . . . . 6
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7 | simpl 108 |
. . . . . . . . 9
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8 | simplr 520 |
. . . . . . . . . 10
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9 | simpr 109 |
. . . . . . . . . . 11
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10 | ancom 264 |
. . . . . . . . . . . . 13
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11 | 10 | notbii 658 |
. . . . . . . . . . . 12
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12 | imnan 680 |
. . . . . . . . . . . 12
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13 | 11, 12 | bitr4i 186 |
. . . . . . . . . . 11
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14 | 9, 13 | sylib 121 |
. . . . . . . . . 10
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15 | 8, 14 | mpd 13 |
. . . . . . . . 9
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16 | 7, 15, 8 | jca32 308 |
. . . . . . . 8
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17 | eldif 3085 |
. . . . . . . . . 10
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18 | 17 | anbi1i 454 |
. . . . . . . . 9
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19 | anandir 581 |
. . . . . . . . 9
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20 | 18, 19 | bitri 183 |
. . . . . . . 8
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21 | 16, 20 | sylibr 133 |
. . . . . . 7
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22 | 21 | eximi 1580 |
. . . . . 6
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23 | 6, 22 | syl 14 |
. . . . 5
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24 | df-rex 2423 |
. . . . 5
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25 | 23, 24 | sylibr 133 |
. . . 4
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26 | 1, 3, 25 | syl2anb 289 |
. . 3
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27 | 26 | ss2abi 3174 |
. 2
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28 | dfima2 4891 |
. . . 4
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29 | dfima2 4891 |
. . . 4
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30 | 28, 29 | difeq12i 3197 |
. . 3
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31 | difab 3350 |
. . 3
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32 | 30, 31 | eqtri 2161 |
. 2
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33 | dfima2 4891 |
. 2
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34 | 27, 32, 33 | 3sstr4i 3143 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-fal 1338 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-rab 2426 df-v 2691 df-dif 3078 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-br 3938 df-opab 3998 df-xp 4553 df-cnv 4555 df-dm 4557 df-rn 4558 df-res 4559 df-ima 4560 |
This theorem is referenced by: imadif 5211 |
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