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Mirrors > Home > NFE Home > Th. List > 2reuswap | 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 |
---|---|
2reuswap |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rmo 2623 |
. . 3
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2 | 1 | ralbii 2639 |
. 2
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3 | df-ral 2620 |
. . . 4
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4 | moanimv 2262 |
. . . . 5
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5 | 4 | albii 1566 |
. . . 4
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6 | 3, 5 | bitr4i 243 |
. . 3
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7 | 2euswap 2280 |
. . . 4
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8 | df-reu 2622 |
. . . . 5
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9 | r19.42v 2766 |
. . . . . . . 8
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10 | df-rex 2621 |
. . . . . . . 8
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11 | 9, 10 | bitr3i 242 |
. . . . . . 7
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12 | an12 772 |
. . . . . . . 8
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13 | 12 | exbii 1582 |
. . . . . . 7
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14 | 11, 13 | bitri 240 |
. . . . . 6
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15 | 14 | eubii 2213 |
. . . . 5
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16 | 8, 15 | bitri 240 |
. . . 4
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17 | df-reu 2622 |
. . . . 5
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18 | r19.42v 2766 |
. . . . . . 7
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19 | df-rex 2621 |
. . . . . . 7
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20 | 18, 19 | bitr3i 242 |
. . . . . 6
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21 | 20 | eubii 2213 |
. . . . 5
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22 | 17, 21 | bitri 240 |
. . . 4
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23 | 7, 16, 22 | 3imtr4g 261 |
. . 3
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24 | 6, 23 | sylbi 187 |
. 2
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25 | 2, 24 | sylbi 187 |
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 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-eu 2208 df-mo 2209 df-ral 2620 df-rex 2621 df-reu 2622 df-rmo 2623 |
This theorem is referenced by: (None) |
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