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Mirrors > Home > MPE Home > Th. List > suppvalbr | Structured version Visualization version Unicode version |
Description: The value of the operation constructing the support of a function expressed by binary relations. (Contributed by AV, 7-Apr-2019.) |
Ref | Expression |
---|---|
suppvalbr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | suppval 6913 |
. 2
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2 | df-rab 2745 |
. . . 4
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3 | vex 3047 |
. . . . . . 7
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4 | 3 | eldm 5031 |
. . . . . 6
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5 | df-sn 3968 |
. . . . . . . 8
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6 | 5 | neeq2i 2688 |
. . . . . . 7
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7 | imasng 5189 |
. . . . . . . . 9
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8 | 3, 7 | ax-mp 5 |
. . . . . . . 8
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9 | 8 | neeq1i 2687 |
. . . . . . 7
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10 | nabbi 2724 |
. . . . . . 7
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11 | 6, 9, 10 | 3bitr4i 281 |
. . . . . 6
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12 | 4, 11 | anbi12i 702 |
. . . . 5
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13 | 12 | abbii 2566 |
. . . 4
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14 | 2, 13 | eqtri 2472 |
. . 3
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15 | 14 | a1i 11 |
. 2
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16 | df-ne 2623 |
. . . . . . . 8
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17 | 16 | bicomi 206 |
. . . . . . 7
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18 | 17 | bibi2i 315 |
. . . . . 6
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19 | 18 | exbii 1717 |
. . . . 5
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20 | 19 | anbi2i 699 |
. . . 4
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21 | 20 | abbii 2566 |
. . 3
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22 | 21 | a1i 11 |
. 2
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23 | 1, 15, 22 | 3eqtrd 2488 |
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 1668 ax-4 1681 ax-5 1757 ax-6 1804 ax-7 1850 ax-8 1888 ax-9 1895 ax-10 1914 ax-11 1919 ax-12 1932 ax-13 2090 ax-ext 2430 ax-sep 4524 ax-nul 4533 ax-pr 4638 ax-un 6580 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 986 df-tru 1446 df-ex 1663 df-nf 1667 df-sb 1797 df-eu 2302 df-mo 2303 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2580 df-ne 2623 df-ral 2741 df-rex 2742 df-rab 2745 df-v 3046 df-sbc 3267 df-dif 3406 df-un 3408 df-in 3410 df-ss 3417 df-nul 3731 df-if 3881 df-sn 3968 df-pr 3970 df-op 3974 df-uni 4198 df-br 4402 df-opab 4461 df-id 4748 df-xp 4839 df-rel 4840 df-cnv 4841 df-co 4842 df-dm 4843 df-rn 4844 df-res 4845 df-ima 4846 df-iota 5545 df-fun 5583 df-fv 5589 df-ov 6291 df-oprab 6292 df-mpt2 6293 df-supp 6912 |
This theorem is referenced by: suppimacnvss 6921 suppimacnv 6922 |
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