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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 4563 |
. . . 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 6389 |
. . . 4
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6 | 5 | adantl 271 |
. . 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 6390 |
. . . 4
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11 | 10 | adantl 271 |
. . 3
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12 | 4 | adantl 271 |
. . . . . . . . . . 11
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13 | simpll 496 |
. . . . . . . . . . 11
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14 | simplr 497 |
. . . . . . . . . . 11
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15 | 12, 13, 14 | caovcomd 5801 |
. . . . . . . . . 10
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16 | 1 | ecopoveq 6385 |
. . . . . . . . . 10
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17 | 15, 16 | mpbird 165 |
. . . . . . . . 9
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18 | 17 | anidms 389 |
. . . . . . . 8
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19 | 18 | rgen2a 2429 |
. . . . . . 7
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20 | breq12 3850 |
. . . . . . . . 9
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21 | 20 | anidms 389 |
. . . . . . . 8
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22 | 21 | ralxp 4579 |
. . . . . . 7
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23 | 19, 22 | mpbir 144 |
. . . . . 6
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24 | 23 | rspec 2427 |
. . . . 5
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25 | 24 | a1i 9 |
. . . 4
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26 | opabssxp 4512 |
. . . . . . 7
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27 | 1, 26 | eqsstri 3056 |
. . . . . 6
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28 | 27 | ssbri 3887 |
. . . . 5
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29 | brxp 4468 |
. . . . . 6
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30 | 29 | simplbi 268 |
. . . . 5
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31 | 28, 30 | syl 14 |
. . . 4
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32 | 25, 31 | impbid1 140 |
. . 3
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33 | 3, 6, 11, 32 | iserd 6316 |
. 2
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34 | 33 | mptru 1298 |
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 104 ax-ia2 105 ax-ia3 106 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-14 1450 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-sep 3957 ax-pow 4009 ax-pr 4036 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-nf 1395 df-sb 1693 df-eu 1951 df-mo 1952 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ral 2364 df-rex 2365 df-v 2621 df-sbc 2841 df-csb 2934 df-un 3003 df-in 3005 df-ss 3012 df-pw 3431 df-sn 3452 df-pr 3453 df-op 3455 df-uni 3654 df-iun 3732 df-br 3846 df-opab 3900 df-xp 4444 df-rel 4445 df-cnv 4446 df-co 4447 df-dm 4448 df-iota 4980 df-fv 5023 df-ov 5655 df-er 6290 |
This theorem is referenced by: enqer 6915 enrer 7279 |
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