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Mirrors > Home > ILE Home > Th. List > imadiflem | Unicode version |
Description: One direction of imadif 5315. This direction does not require
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Ref | Expression |
---|---|
imadiflem |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2474 |
. . . 4
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2 | df-rex 2474 |
. . . . 5
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3 | 2 | notbii 669 |
. . . 4
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4 | alnex 1510 |
. . . . . . 7
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5 | 19.29r 1632 |
. . . . . . 7
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6 | 4, 5 | sylan2br 288 |
. . . . . 6
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7 | simpl 109 |
. . . . . . . . 9
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8 | simplr 528 |
. . . . . . . . . 10
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9 | simpr 110 |
. . . . . . . . . . 11
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10 | ancom 266 |
. . . . . . . . . . . . 13
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11 | 10 | notbii 669 |
. . . . . . . . . . . 12
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12 | imnan 691 |
. . . . . . . . . . . 12
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13 | 11, 12 | bitr4i 187 |
. . . . . . . . . . 11
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14 | 9, 13 | sylib 122 |
. . . . . . . . . 10
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15 | 8, 14 | mpd 13 |
. . . . . . . . 9
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16 | 7, 15, 8 | jca32 310 |
. . . . . . . 8
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17 | eldif 3153 |
. . . . . . . . . 10
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18 | 17 | anbi1i 458 |
. . . . . . . . 9
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19 | anandir 591 |
. . . . . . . . 9
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20 | 18, 19 | bitri 184 |
. . . . . . . 8
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21 | 16, 20 | sylibr 134 |
. . . . . . 7
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22 | 21 | eximi 1611 |
. . . . . 6
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23 | 6, 22 | syl 14 |
. . . . 5
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24 | df-rex 2474 |
. . . . 5
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25 | 23, 24 | sylibr 134 |
. . . 4
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26 | 1, 3, 25 | syl2anb 291 |
. . 3
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27 | 26 | ss2abi 3242 |
. 2
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28 | dfima2 4990 |
. . . 4
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29 | dfima2 4990 |
. . . 4
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30 | 28, 29 | difeq12i 3266 |
. . 3
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31 | difab 3419 |
. . 3
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32 | 30, 31 | eqtri 2210 |
. 2
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33 | dfima2 4990 |
. 2
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34 | 27, 32, 33 | 3sstr4i 3211 |
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 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4192 ax-pr 4227 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-rab 2477 df-v 2754 df-dif 3146 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-br 4019 df-opab 4080 df-xp 4650 df-cnv 4652 df-dm 4654 df-rn 4655 df-res 4656 df-ima 4657 |
This theorem is referenced by: imadif 5315 |
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