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Theorem eueq 3198
 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 2492 . . . 4
21gen2 1678 . . 3
32biantru 513 . 2
4 isset 3035 . 2
5 eqeq1 2475 . . 3
65eu4 2367 . 2
73, 4, 63bitr4i 285 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189   wa 376  wal 1450   wceq 1452  wex 1671   wcel 1904  weu 2319  cvv 3031 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-mo 2324  df-clab 2458  df-cleq 2464  df-clel 2467  df-v 3033 This theorem is referenced by:  eueq1  3199  moeq  3202  reuhypd  4627  mptfnf  5709  mptfng  5713  upxp  20715  iotasbc  36840
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