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Mirrors > Home > ILE Home > Th. List > imadiflem | Unicode version |
Description: One direction of imadif 5107. This direction does not require
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Ref | Expression |
---|---|
imadiflem |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2366 |
. . . 4
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2 | df-rex 2366 |
. . . . 5
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3 | 2 | notbii 630 |
. . . 4
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4 | alnex 1434 |
. . . . . . 7
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5 | 19.29r 1558 |
. . . . . . 7
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6 | 4, 5 | sylan2br 283 |
. . . . . 6
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7 | simpl 108 |
. . . . . . . . 9
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8 | simplr 498 |
. . . . . . . . . 10
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9 | simpr 109 |
. . . . . . . . . . 11
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10 | ancom 263 |
. . . . . . . . . . . . 13
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11 | 10 | notbii 630 |
. . . . . . . . . . . 12
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12 | imnan 660 |
. . . . . . . . . . . 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 304 |
. . . . . . . 8
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17 | eldif 3009 |
. . . . . . . . . 10
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18 | 17 | anbi1i 447 |
. . . . . . . . 9
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19 | anandir 559 |
. . . . . . . . 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 1537 |
. . . . . 6
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23 | 6, 22 | syl 14 |
. . . . 5
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24 | df-rex 2366 |
. . . . 5
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25 | 23, 24 | sylibr 133 |
. . . 4
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26 | 1, 3, 25 | syl2anb 286 |
. . 3
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27 | 26 | ss2abi 3094 |
. 2
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28 | dfima2 4789 |
. . . 4
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29 | dfima2 4789 |
. . . 4
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30 | 28, 29 | difeq12i 3117 |
. . 3
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31 | difab 3269 |
. . 3
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32 | 30, 31 | eqtri 2109 |
. 2
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33 | dfima2 4789 |
. 2
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34 | 27, 32, 33 | 3sstr4i 3066 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 580 ax-in2 581 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-14 1451 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-sep 3963 ax-pow 4015 ax-pr 4045 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-fal 1296 df-nf 1396 df-sb 1694 df-eu 1952 df-mo 1953 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-ral 2365 df-rex 2366 df-rab 2369 df-v 2622 df-dif 3002 df-un 3004 df-in 3006 df-ss 3013 df-pw 3435 df-sn 3456 df-pr 3457 df-op 3459 df-br 3852 df-opab 3906 df-xp 4457 df-cnv 4459 df-dm 4461 df-rn 4462 df-res 4463 df-ima 4464 |
This theorem is referenced by: imadif 5107 |
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