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Mirrors > Home > ILE Home > Th. List > ecopovsym | Unicode version |
Description: Assuming the operation
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Ref | Expression |
---|---|
ecopopr.1 |
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ecopopr.com |
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Ref | Expression |
---|---|
ecopovsym |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ecopopr.1 |
. . . . 5
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2 | opabssxp 4715 |
. . . . 5
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3 | 1, 2 | eqsstri 3202 |
. . . 4
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4 | 3 | brel 4693 |
. . 3
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5 | eqid 2189 |
. . . 4
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6 | breq1 4021 |
. . . . 5
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7 | breq2 4022 |
. . . . 5
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8 | 6, 7 | bibi12d 235 |
. . . 4
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9 | breq2 4022 |
. . . . 5
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10 | breq1 4021 |
. . . . 5
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11 | 9, 10 | bibi12d 235 |
. . . 4
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12 | 1 | ecopoveq 6648 |
. . . . . 6
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13 | vex 2755 |
. . . . . . . . 9
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14 | vex 2755 |
. . . . . . . . 9
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15 | ecopopr.com |
. . . . . . . . 9
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16 | 13, 14, 15 | caovcom 6049 |
. . . . . . . 8
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17 | vex 2755 |
. . . . . . . . 9
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18 | vex 2755 |
. . . . . . . . 9
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19 | 17, 18, 15 | caovcom 6049 |
. . . . . . . 8
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20 | 16, 19 | eqeq12i 2203 |
. . . . . . 7
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21 | eqcom 2191 |
. . . . . . 7
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22 | 20, 21 | bitri 184 |
. . . . . 6
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23 | 12, 22 | bitrdi 196 |
. . . . 5
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24 | 1 | ecopoveq 6648 |
. . . . . 6
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25 | 24 | ancoms 268 |
. . . . 5
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26 | 23, 25 | bitr4d 191 |
. . . 4
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27 | 5, 8, 11, 26 | 2optocl 4718 |
. . 3
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28 | 4, 27 | syl 14 |
. 2
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29 | 28 | ibi 176 |
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-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-opab 4080 df-xp 4647 df-iota 5193 df-fv 5239 df-ov 5894 |
This theorem is referenced by: ecopover 6651 |
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