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Mirrors > Home > NFE Home > Th. List > eluniab | Unicode version |
Description: Membership in union of a class abstraction. (Contributed by NM, 11-Aug-1994.) (Revised by Mario Carneiro, 14-Nov-2016.) |
Ref | Expression |
---|---|
eluniab |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eluni 3895 |
. 2
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2 | nfv 1619 |
. . . 4
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3 | nfsab1 2343 |
. . . 4
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4 | 2, 3 | nfan 1824 |
. . 3
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5 | nfv 1619 |
. . 3
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6 | eleq2 2414 |
. . . 4
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7 | eleq1 2413 |
. . . . 5
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8 | abid 2341 |
. . . . 5
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9 | 7, 8 | syl6bb 252 |
. . . 4
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10 | 6, 9 | anbi12d 691 |
. . 3
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11 | 4, 5, 10 | cbvex 1985 |
. 2
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12 | 1, 11 | bitri 240 |
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 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 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-v 2862 df-uni 3893 |
This theorem is referenced by: elunirab 3905 dfiun2g 4000 eqtfinrelk 4487 elfv 5327 funiunfv 5468 tcfnex 6245 |
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