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Mirrors > Home > MPE Home > Th. List > euabsn2 | Structured version Visualization version Unicode version |
Description: Another way to express existential uniqueness of a wff: its class abstraction is a singleton. (Contributed by Mario Carneiro, 14-Nov-2016.) |
Ref | Expression |
---|---|
euabsn2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-eu 2323 |
. 2
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2 | abeq1 2581 |
. . . 4
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3 | elsn 3973 |
. . . . . 6
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4 | 3 | bibi2i 320 |
. . . . 5
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5 | 4 | albii 1699 |
. . . 4
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6 | 2, 5 | bitri 257 |
. . 3
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7 | 6 | exbii 1726 |
. 2
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8 | 1, 7 | bitr4i 260 |
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 ax-ext 2451 |
This theorem depends on definitions: df-bi 190 df-an 378 df-tru 1455 df-ex 1672 df-nf 1676 df-sb 1806 df-eu 2323 df-clab 2458 df-cleq 2464 df-clel 2467 df-sn 3960 |
This theorem is referenced by: euabsn 4035 reusn 4036 absneu 4037 uniintab 4264 eusvobj2 6301 |
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