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Mirrors > Home > MPE Home > Th. List > elvvv | Structured version Visualization version Unicode version |
Description: Membership in universal class of ordered triples. (Contributed by NM, 17-Dec-2008.) |
Ref | Expression |
---|---|
elvvv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elxp 4870 |
. 2
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2 | anass 659 |
. . . . 5
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3 | 19.42vv 1847 |
. . . . . 6
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4 | ancom 456 |
. . . . . . 7
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5 | 4 | 2exbii 1730 |
. . . . . 6
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6 | vex 3060 |
. . . . . . . 8
![]() ![]() ![]() ![]() | |
7 | 6 | biantru 512 |
. . . . . . 7
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8 | elvv 4912 |
. . . . . . . 8
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9 | 8 | anbi2i 705 |
. . . . . . 7
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10 | 7, 9 | bitr3i 259 |
. . . . . 6
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11 | 3, 5, 10 | 3bitr4ri 286 |
. . . . 5
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12 | 2, 11 | bitr3i 259 |
. . . 4
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13 | 12 | 2exbii 1730 |
. . 3
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14 | exrot4 1943 |
. . . 4
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15 | excom 1938 |
. . . . . 6
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16 | opex 4678 |
. . . . . . . 8
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17 | opeq1 4180 |
. . . . . . . . 9
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18 | 17 | eqeq2d 2472 |
. . . . . . . 8
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19 | 16, 18 | ceqsexv 3096 |
. . . . . . 7
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20 | 19 | exbii 1729 |
. . . . . 6
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21 | 15, 20 | bitri 257 |
. . . . 5
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22 | 21 | 2exbii 1730 |
. . . 4
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23 | 14, 22 | bitr3i 259 |
. . 3
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24 | 13, 23 | bitri 257 |
. 2
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25 | 1, 24 | bitri 257 |
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 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-9 1907 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 ax-sep 4539 ax-nul 4548 ax-pr 4653 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 993 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-ne 2635 df-rab 2758 df-v 3059 df-dif 3419 df-un 3421 df-in 3423 df-ss 3430 df-nul 3744 df-if 3894 df-sn 3981 df-pr 3983 df-op 3987 df-opab 4476 df-xp 4859 |
This theorem is referenced by: ssrelrel 4954 dftpos3 7017 |
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