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Theorem reu6i 2879
 Description: A condition which implies existential uniqueness. (Contributed by Mario Carneiro, 2-Oct-2015.)
Assertion
Ref Expression
reu6i
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem reu6i
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eqeq2 2150 . . . . 5
21bibi2d 231 . . . 4
32ralbidv 2438 . . 3
43rspcev 2793 . 2
5 reu6 2877 . 2
64, 5sylibr 133 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1332   wcel 1481  wral 2417  wrex 2418  wreu 2419 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-eu 2003  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-rex 2423  df-reu 2424  df-v 2691 This theorem is referenced by:  eqreu  2880  riota5f  5762  negeu  7978  creur  8742  creui  8743
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