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Mirrors > Home > ILE Home > Th. List > 2reuswapdc | Unicode version |
Description: A condition allowing swap of uniqueness and existential quantifiers. (Contributed by Thierry Arnoux, 7-Apr-2017.) (Revised by NM, 16-Jun-2017.) |
Ref | Expression |
---|---|
2reuswapdc |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rmo 2378 |
. . 3
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2 | 1 | ralbii 2395 |
. 2
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3 | df-ral 2375 |
. . . 4
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4 | moanimv 2030 |
. . . . 5
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5 | 4 | albii 1411 |
. . . 4
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6 | 3, 5 | bitr4i 186 |
. . 3
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7 | df-reu 2377 |
. . . . . 6
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8 | r19.42v 2538 |
. . . . . . . . 9
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9 | df-rex 2376 |
. . . . . . . . 9
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10 | 8, 9 | bitr3i 185 |
. . . . . . . 8
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11 | an12 529 |
. . . . . . . . 9
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12 | 11 | exbii 1548 |
. . . . . . . 8
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13 | 10, 12 | bitri 183 |
. . . . . . 7
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14 | 13 | eubii 1964 |
. . . . . 6
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15 | 7, 14 | bitri 183 |
. . . . 5
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16 | 2euswapdc 2046 |
. . . . 5
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17 | 15, 16 | syl7bi 164 |
. . . 4
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18 | df-reu 2377 |
. . . . . 6
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19 | r19.42v 2538 |
. . . . . . . 8
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20 | df-rex 2376 |
. . . . . . . 8
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21 | 19, 20 | bitr3i 185 |
. . . . . . 7
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22 | 21 | eubii 1964 |
. . . . . 6
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23 | 18, 22 | bitri 183 |
. . . . 5
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24 | 23 | imbi2i 225 |
. . . 4
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25 | 17, 24 | syl6ibr 161 |
. . 3
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26 | 6, 25 | syl5bi 151 |
. 2
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27 | 2, 26 | syl5bi 151 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 582 ax-in2 583 ax-io 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 |
This theorem depends on definitions: df-bi 116 df-dc 784 df-tru 1299 df-nf 1402 df-sb 1700 df-eu 1958 df-mo 1959 df-ral 2375 df-rex 2376 df-reu 2377 df-rmo 2378 |
This theorem is referenced by: (None) |
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