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Mirrors > Home > ILE Home > Th. List > euex | Unicode version |
Description: Existential uniqueness implies existence. (Contributed by NM, 15-Sep-1993.) (Proof shortened by Andrew Salmon, 9-Jul-2011.) |
Ref | Expression |
---|---|
euex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-17 1416 |
. . 3
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2 | 1 | eu1 1922 |
. 2
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3 | exsimpl 1505 |
. 2
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4 | 2, 3 | sylbi 114 |
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-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-nf 1347 df-sb 1643 df-eu 1900 |
This theorem is referenced by: eu2 1941 eu3h 1942 eu5 1944 exmoeudc 1960 eupickbi 1979 2eu2ex 1986 euxfrdc 2721 repizf 3864 eusvnf 4151 eusvnfb 4152 tz6.12c 5146 ndmfvg 5147 nfvres 5149 0fv 5151 eusvobj2 5441 fnoprabg 5544 |
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