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Mirrors > Home > MPE Home > Th. List > reu2 | Structured version Visualization version Unicode version |
Description: A way to express restricted uniqueness. (Contributed by NM, 22-Nov-1994.) |
Ref | Expression |
---|---|
reu2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1772 |
. . 3
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2 | 1 | eu2 2349 |
. 2
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3 | df-reu 2756 |
. 2
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4 | df-rex 2755 |
. . 3
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5 | df-ral 2754 |
. . . 4
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6 | 19.21v 1797 |
. . . . . 6
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7 | nfv 1772 |
. . . . . . . . . . . . 13
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8 | nfs1v 2277 |
. . . . . . . . . . . . 13
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9 | 7, 8 | nfan 2022 |
. . . . . . . . . . . 12
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10 | eleq1 2528 |
. . . . . . . . . . . . 13
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11 | sbequ12 2094 |
. . . . . . . . . . . . 13
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12 | 10, 11 | anbi12d 722 |
. . . . . . . . . . . 12
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13 | 9, 12 | sbie 2248 |
. . . . . . . . . . 11
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14 | 13 | anbi2i 705 |
. . . . . . . . . 10
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15 | an4 838 |
. . . . . . . . . 10
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16 | 14, 15 | bitri 257 |
. . . . . . . . 9
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17 | 16 | imbi1i 331 |
. . . . . . . 8
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18 | impexp 452 |
. . . . . . . 8
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19 | impexp 452 |
. . . . . . . 8
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20 | 17, 18, 19 | 3bitri 279 |
. . . . . . 7
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21 | 20 | albii 1702 |
. . . . . 6
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22 | df-ral 2754 |
. . . . . . 7
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23 | 22 | imbi2i 318 |
. . . . . 6
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24 | 6, 21, 23 | 3bitr4i 285 |
. . . . 5
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25 | 24 | albii 1702 |
. . . 4
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26 | 5, 25 | bitr4i 260 |
. . 3
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27 | 4, 26 | anbi12i 708 |
. 2
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28 | 2, 3, 27 | 3bitr4i 285 |
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-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-eu 2314 df-mo 2315 df-cleq 2455 df-clel 2458 df-ral 2754 df-rex 2755 df-reu 2756 |
This theorem is referenced by: reu2eqd 3247 disjinfi 37506 |
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