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Theorem eueq 2773
 Description: Equality has existential uniqueness. (Contributed by NM, 25-Nov-1994.)
Assertion
Ref Expression
eueq
Distinct variable group:   ,

Proof of Theorem eueq
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eqtr3 2102 . . . 4
21gen2 1380 . . 3
32biantru 296 . 2
4 isset 2614 . 2
5 eqeq1 2089 . . 3
65eu4 2005 . 2
73, 4, 63bitr4i 210 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103  wal 1283   wceq 1285  wex 1422   wcel 1434  weu 1943  cvv 2610 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  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1688  df-eu 1946  df-mo 1947  df-clab 2070  df-cleq 2076  df-clel 2079  df-v 2612 This theorem is referenced by:  eueq1  2774  moeq  2777  mosubt  2779  reuhypd  4250  mptfng  5076
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