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Mirrors > Home > MPE Home > Th. List > rabasiun | Structured version Visualization version Unicode version |
Description: A class abstraction with a restricted existential quantification expressed as indexed union. (Contributed by Alexander van der Vekens, 29-Jul-2018.) |
Ref | Expression |
---|---|
rabasiun |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2602 |
. . . . . 6
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2 | 1 | nfcri 2596 |
. . . . 5
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3 | nfv 1771 |
. . . . 5
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4 | 2, 3 | nfan 2021 |
. . . 4
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5 | nfcv 2602 |
. . . . . 6
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6 | 5 | nfcri 2596 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() |
7 | nfcv 2602 |
. . . . . 6
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8 | nfs1v 2276 |
. . . . . 6
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9 | 7, 8 | nfrex 2861 |
. . . . 5
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10 | 6, 9 | nfan 2021 |
. . . 4
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11 | eleq1 2527 |
. . . . 5
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12 | sbequ12 2093 |
. . . . . 6
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13 | 12 | rexbidv 2912 |
. . . . 5
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14 | 11, 13 | anbi12d 722 |
. . . 4
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15 | 4, 10, 14 | cbvab 2584 |
. . 3
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16 | r19.42v 2956 |
. . . . 5
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17 | nfcv 2602 |
. . . . . . . 8
![]() ![]() ![]() ![]() | |
18 | 17, 5, 8, 12 | elrabf 3205 |
. . . . . . 7
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19 | 18 | bicomi 207 |
. . . . . 6
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20 | 19 | rexbii 2900 |
. . . . 5
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21 | 16, 20 | bitr3i 259 |
. . . 4
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22 | 21 | abbii 2577 |
. . 3
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23 | 15, 22 | eqtri 2483 |
. 2
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24 | df-rab 2757 |
. 2
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25 | df-iun 4293 |
. 2
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26 | 23, 24, 25 | 3eqtr4i 2493 |
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 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-10 1925 ax-11 1930 ax-12 1943 ax-13 2101 ax-ext 2441 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-tru 1457 df-ex 1674 df-nf 1678 df-sb 1808 df-clab 2448 df-cleq 2454 df-clel 2457 df-nfc 2591 df-ral 2753 df-rex 2754 df-rab 2757 df-v 3058 df-iun 4293 |
This theorem is referenced by: hashrabrex 13931 |
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