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Mathbox for Thierry Arnoux |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > 2reuswap2 | Structured version Visualization version Unicode version |
Description: A condition allowing swap of uniqueness and existential quantifiers. (Contributed by Thierry Arnoux, 7-Apr-2017.) |
Ref | Expression |
---|---|
2reuswap2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2761 |
. . 3
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2 | moanimv 2380 |
. . . 4
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3 | 2 | albii 1699 |
. . 3
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4 | 1, 3 | bitr4i 260 |
. 2
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5 | 2euswap 2397 |
. . 3
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6 | df-reu 2763 |
. . . 4
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7 | r19.42v 2931 |
. . . . . . 7
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8 | df-rex 2762 |
. . . . . . 7
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9 | 7, 8 | bitr3i 259 |
. . . . . 6
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10 | an12 814 |
. . . . . . 7
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11 | 10 | exbii 1726 |
. . . . . 6
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12 | 9, 11 | bitri 257 |
. . . . 5
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13 | 12 | eubii 2341 |
. . . 4
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14 | 6, 13 | bitri 257 |
. . 3
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15 | df-reu 2763 |
. . . 4
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16 | r19.42v 2931 |
. . . . . 6
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17 | df-rex 2762 |
. . . . . 6
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18 | 16, 17 | bitr3i 259 |
. . . . 5
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19 | 18 | eubii 2341 |
. . . 4
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20 | 15, 19 | bitri 257 |
. . 3
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21 | 5, 14, 20 | 3imtr4g 278 |
. 2
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22 | 4, 21 | sylbi 200 |
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 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 |
This theorem depends on definitions: df-bi 190 df-or 377 df-an 378 df-tru 1455 df-ex 1672 df-nf 1676 df-eu 2323 df-mo 2324 df-ral 2761 df-rex 2762 df-reu 2763 |
This theorem is referenced by: reuxfr3d 28204 |
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