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Theorem eueq 3271
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 2485 . . . 4
21gen2 1619 . . 3
32biantru 505 . 2
4 isset 3113 . 2
5 eqeq1 2461 . . 3
65eu4 2338 . 2
73, 4, 63bitr4i 277 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  E.wex 1612  e.wcel 1818  E!weu 2282   cvv 3109
This theorem is referenced by:  eueq1  3272  moeq  3275  reuhypd  4679  mptfng  5711  upxp  20124  mptfnf  27499  iotasbc  31326
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111
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