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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 1465 |
. . 3
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2 | 1 | eu1 1974 |
. 2
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3 | exsimpl 1554 |
. 2
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4 | 2, 3 | sylbi 120 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 |
This theorem depends on definitions: df-bi 116 df-nf 1396 df-sb 1694 df-eu 1952 |
This theorem is referenced by: eu2 1993 eu3h 1994 eu5 1996 exmoeudc 2012 eupickbi 2031 2eu2ex 2038 euxfrdc 2802 repizf 3961 eusvnf 4288 eusvnfb 4289 tz6.12c 5347 ndmfvg 5348 nfvres 5350 0fv 5352 eusvobj2 5652 fnoprabg 5760 |
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