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Theorem eupick 2022
 Description: Existential uniqueness "picks" a variable value for which another wff is true. If there is only one thing such that is true, and there is also an (actually the same one) such that and are both true, then implies regardless of . This theorem can be useful for eliminating existential quantifiers in a hypothesis. Compare Theorem *14.26 in [WhiteheadRussell] p. 192. (Contributed by NM, 10-Jul-1994.)
Assertion
Ref Expression
eupick

Proof of Theorem eupick
StepHypRef Expression
1 eumo 1975 . 2
2 mopick 2021 . 2
31, 2sylan 277 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102  wex 1422  weu 1943  wmo 1944 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469 This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1688  df-eu 1946  df-mo 1947 This theorem is referenced by:  eupicka  2023  eupickb  2024  reupick  3264  reupick3  3265  copsexg  4027  eusv2nf  4234  funssres  4992  oprabid  5588
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