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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 2308 |
. . 3
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2 | 1 | ralbii 2324 |
. 2
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3 | df-ral 2305 |
. . . 4
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4 | moanimv 1972 |
. . . . 5
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5 | 4 | albii 1356 |
. . . 4
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6 | 3, 5 | bitr4i 176 |
. . 3
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7 | df-reu 2307 |
. . . . . 6
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8 | r19.42v 2461 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9 | df-rex 2306 |
. . . . . . . . 9
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10 | 8, 9 | bitr3i 175 |
. . . . . . . 8
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11 | an12 495 |
. . . . . . . . 9
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12 | 11 | exbii 1493 |
. . . . . . . 8
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13 | 10, 12 | bitri 173 |
. . . . . . 7
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14 | 13 | eubii 1906 |
. . . . . 6
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15 | 7, 14 | bitri 173 |
. . . . 5
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16 | 2euswapdc 1988 |
. . . . 5
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17 | 15, 16 | syl7bi 154 |
. . . 4
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18 | df-reu 2307 |
. . . . . 6
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19 | r19.42v 2461 |
. . . . . . . 8
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20 | df-rex 2306 |
. . . . . . . 8
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21 | 19, 20 | bitr3i 175 |
. . . . . . 7
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22 | 21 | eubii 1906 |
. . . . . 6
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23 | 18, 22 | bitri 173 |
. . . . 5
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24 | 23 | imbi2i 215 |
. . . 4
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25 | 17, 24 | syl6ibr 151 |
. . 3
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26 | 6, 25 | syl5bi 141 |
. 2
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27 | 2, 26 | syl5bi 141 |
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 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 |
This theorem depends on definitions: df-bi 110 df-dc 742 df-tru 1245 df-nf 1347 df-sb 1643 df-eu 1900 df-mo 1901 df-ral 2305 df-rex 2306 df-reu 2307 df-rmo 2308 |
This theorem is referenced by: (None) |
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