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Mirrors > Home > ILE Home > Th. List > ecopoverg | Unicode version |
Description: Assuming that operation
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Ref | Expression |
---|---|
ecopopr.1 |
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ecopoprg.com |
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ecopoprg.cl |
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ecopoprg.ass |
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ecopoprg.can |
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Ref | Expression |
---|---|
ecopoverg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ecopopr.1 |
. . . . 5
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2 | 1 | relopabi 4406 |
. . . 4
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3 | 2 | a1i 9 |
. . 3
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4 | ecopoprg.com |
. . . . 5
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5 | 1, 4 | ecopovsymg 6141 |
. . . 4
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6 | 5 | adantl 262 |
. . 3
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7 | ecopoprg.cl |
. . . . 5
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8 | ecopoprg.ass |
. . . . 5
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9 | ecopoprg.can |
. . . . 5
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10 | 1, 4, 7, 8, 9 | ecopovtrng 6142 |
. . . 4
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11 | 10 | adantl 262 |
. . 3
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12 | 4 | adantl 262 |
. . . . . . . . . . 11
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13 | simpll 481 |
. . . . . . . . . . 11
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14 | simplr 482 |
. . . . . . . . . . 11
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15 | 12, 13, 14 | caovcomd 5599 |
. . . . . . . . . 10
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16 | 1 | ecopoveq 6137 |
. . . . . . . . . 10
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17 | 15, 16 | mpbird 156 |
. . . . . . . . 9
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18 | 17 | anidms 377 |
. . . . . . . 8
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19 | 18 | rgen2a 2369 |
. . . . . . 7
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20 | breq12 3760 |
. . . . . . . . 9
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21 | 20 | anidms 377 |
. . . . . . . 8
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22 | 21 | ralxp 4422 |
. . . . . . 7
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23 | 19, 22 | mpbir 134 |
. . . . . 6
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24 | 23 | rspec 2367 |
. . . . 5
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25 | 24 | a1i 9 |
. . . 4
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26 | opabssxp 4357 |
. . . . . . 7
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27 | 1, 26 | eqsstri 2969 |
. . . . . 6
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28 | 27 | ssbri 3797 |
. . . . 5
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29 | brxp 4318 |
. . . . . 6
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30 | 29 | simplbi 259 |
. . . . 5
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31 | 28, 30 | syl 14 |
. . . 4
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32 | 25, 31 | impbid1 130 |
. . 3
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33 | 3, 6, 11, 32 | iserd 6068 |
. 2
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34 | 33 | trud 1251 |
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 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-14 1402 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 ax-sep 3866 ax-pow 3918 ax-pr 3935 |
This theorem depends on definitions: df-bi 110 df-3an 886 df-tru 1245 df-nf 1347 df-sb 1643 df-eu 1900 df-mo 1901 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-ral 2305 df-rex 2306 df-v 2553 df-sbc 2759 df-csb 2847 df-un 2916 df-in 2918 df-ss 2925 df-pw 3353 df-sn 3373 df-pr 3374 df-op 3376 df-uni 3572 df-iun 3650 df-br 3756 df-opab 3810 df-xp 4294 df-rel 4295 df-cnv 4296 df-co 4297 df-dm 4298 df-iota 4810 df-fv 4853 df-ov 5458 df-er 6042 |
This theorem is referenced by: enqer 6342 enrer 6663 |
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