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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 4767 |
. . . 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 6652 |
. . . 4
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6 | 5 | adantl 277 |
. . 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 6653 |
. . . 4
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11 | 10 | adantl 277 |
. . 3
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12 | 4 | adantl 277 |
. . . . . . . . . . 11
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13 | simpll 527 |
. . . . . . . . . . 11
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14 | simplr 528 |
. . . . . . . . . . 11
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15 | 12, 13, 14 | caovcomd 6048 |
. . . . . . . . . 10
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16 | 1 | ecopoveq 6648 |
. . . . . . . . . 10
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17 | 15, 16 | mpbird 167 |
. . . . . . . . 9
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18 | 17 | anidms 397 |
. . . . . . . 8
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19 | 18 | rgen2a 2544 |
. . . . . . 7
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20 | breq12 4023 |
. . . . . . . . 9
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21 | 20 | anidms 397 |
. . . . . . . 8
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22 | 21 | ralxp 4785 |
. . . . . . 7
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23 | 19, 22 | mpbir 146 |
. . . . . 6
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24 | 23 | rspec 2542 |
. . . . 5
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25 | 24 | a1i 9 |
. . . 4
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26 | opabssxp 4715 |
. . . . . . 7
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27 | 1, 26 | eqsstri 3202 |
. . . . . 6
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28 | 27 | ssbri 4062 |
. . . . 5
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29 | brxp 4672 |
. . . . . 6
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30 | 29 | simplbi 274 |
. . . . 5
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31 | 28, 30 | syl 14 |
. . . 4
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32 | 25, 31 | impbid1 142 |
. . 3
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33 | 3, 6, 11, 32 | iserd 6579 |
. 2
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34 | 33 | mptru 1373 |
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-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 4189 ax-pr 4224 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 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-v 2754 df-sbc 2978 df-csb 3073 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-iun 3903 df-br 4019 df-opab 4080 df-xp 4647 df-rel 4648 df-cnv 4649 df-co 4650 df-dm 4651 df-iota 5193 df-fv 5239 df-ov 5894 df-er 6553 |
This theorem is referenced by: enqer 7376 enrer 7753 |
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