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Mirrors > Home > NFE Home > Th. List > eluni1g | Unicode version |
Description: Membership in a unit union. (Contributed by SF, 15-Mar-2015.) |
Ref | Expression |
---|---|
eluni1g |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-uni1 4139 |
. . . 4
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2 | 1 | eleq2i 2417 |
. . 3
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3 | eluni 3895 |
. . 3
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4 | elin 3220 |
. . . . . . . 8
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5 | ancom 437 |
. . . . . . . 8
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6 | el1c 4140 |
. . . . . . . . . 10
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7 | 6 | anbi1i 676 |
. . . . . . . . 9
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8 | 19.41v 1901 |
. . . . . . . . 9
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9 | 7, 8 | bitr4i 243 |
. . . . . . . 8
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10 | 4, 5, 9 | 3bitri 262 |
. . . . . . 7
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11 | 10 | anbi2i 675 |
. . . . . 6
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12 | 19.42v 1905 |
. . . . . 6
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13 | 11, 12 | bitr4i 243 |
. . . . 5
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14 | 13 | exbii 1582 |
. . . 4
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15 | excom 1741 |
. . . 4
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16 | an12 772 |
. . . . . . 7
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17 | 16 | exbii 1582 |
. . . . . 6
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18 | snex 4112 |
. . . . . . 7
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19 | eleq2 2414 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
20 | vex 2863 |
. . . . . . . . . 10
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21 | 20 | elsnc2 3763 |
. . . . . . . . 9
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22 | 19, 21 | syl6bb 252 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | eleq1 2413 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
24 | 22, 23 | anbi12d 691 |
. . . . . . 7
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25 | 18, 24 | ceqsexv 2895 |
. . . . . 6
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26 | eqcom 2355 |
. . . . . . 7
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27 | 26 | anbi1i 676 |
. . . . . 6
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28 | 17, 25, 27 | 3bitri 262 |
. . . . 5
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29 | 28 | exbii 1582 |
. . . 4
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30 | 14, 15, 29 | 3bitri 262 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
31 | 2, 3, 30 | 3bitri 262 |
. 2
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32 | sneq 3745 |
. . . 4
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33 | 32 | eleq1d 2419 |
. . 3
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34 | 33 | ceqsexgv 2972 |
. 2
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35 | 31, 34 | syl5bb 248 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 ax-nin 4079 ax-sn 4088 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2479 df-ne 2519 df-v 2862 df-nin 3212 df-compl 3213 df-in 3214 df-un 3215 df-dif 3216 df-ss 3260 df-nul 3552 df-sn 3742 df-uni 3893 df-1c 4137 df-uni1 4139 |
This theorem is referenced by: eluni1 4174 |
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