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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 1537 |
. . 3
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2 | 1 | eu1 2063 |
. 2
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3 | exsimpl 1628 |
. 2
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4 | 2, 3 | sylbi 121 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 df-eu 2041 |
This theorem is referenced by: eu2 2082 eu3h 2083 eu5 2085 exmoeudc 2101 eupickbi 2120 2eu2ex 2127 euxfrdc 2938 repizf 4134 eusvnf 4471 eusvnfb 4472 tz6.12c 5564 ndmfvg 5565 elfvm 5567 nfvres 5568 0fv 5570 eusvobj2 5883 fnoprabg 5998 0g0 12855 txcn 14252 |
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