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Mirrors > Home > ILE Home > Th. List > ecopovsymg | Unicode version |
Description: Assuming the operation
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Ref | Expression |
---|---|
ecopopr.1 |
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ecopoprg.com |
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Ref | Expression |
---|---|
ecopovsymg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ecopopr.1 |
. . . . 5
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2 | opabssxp 4512 |
. . . . 5
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3 | 1, 2 | eqsstri 3056 |
. . . 4
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4 | 3 | brel 4490 |
. . 3
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5 | eqid 2088 |
. . . 4
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6 | breq1 3848 |
. . . . 5
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7 | breq2 3849 |
. . . . 5
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8 | 6, 7 | bibi12d 233 |
. . . 4
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9 | breq2 3849 |
. . . . 5
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10 | breq1 3848 |
. . . . 5
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11 | 9, 10 | bibi12d 233 |
. . . 4
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12 | ecopoprg.com |
. . . . . . . . 9
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13 | 12 | adantl 271 |
. . . . . . . 8
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14 | simpll 496 |
. . . . . . . 8
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15 | simprr 499 |
. . . . . . . 8
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16 | 13, 14, 15 | caovcomd 5801 |
. . . . . . 7
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17 | simplr 497 |
. . . . . . . 8
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18 | simprl 498 |
. . . . . . . 8
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19 | 13, 17, 18 | caovcomd 5801 |
. . . . . . 7
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20 | 16, 19 | eqeq12d 2102 |
. . . . . 6
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21 | eqcom 2090 |
. . . . . 6
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22 | 20, 21 | syl6bb 194 |
. . . . 5
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23 | 1 | ecopoveq 6385 |
. . . . 5
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24 | 1 | ecopoveq 6385 |
. . . . . 6
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25 | 24 | ancoms 264 |
. . . . 5
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26 | 22, 23, 25 | 3bitr4d 218 |
. . . 4
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27 | 5, 8, 11, 26 | 2optocl 4515 |
. . 3
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28 | 4, 27 | syl 14 |
. 2
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29 | 28 | ibi 174 |
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-un 3003 df-in 3005 df-ss 3012 df-pw 3431 df-sn 3452 df-pr 3453 df-op 3455 df-uni 3654 df-br 3846 df-opab 3900 df-xp 4444 df-iota 4980 df-fv 5023 df-ov 5655 |
This theorem is referenced by: ecopoverg 6391 |
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