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Theorem eueq 3241
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 2482 . . . 4
21gen2 1593 . . 3
32biantru 505 . 2
4 isset 3085 . 2
5 eqeq1 2458 . . 3
65eu4 2327 . 2
73, 4, 63bitr4i 277 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1368  =wceq 1370  E.wex 1587  e.wcel 1758  E!weu 2262   cvv 3081
This theorem is referenced by:  eueq1  3242  moeq  3245  reuhypd  4636  mptfng  5655  upxp  19595  mptfnf  26443  iotasbc  30133
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2266  df-mo 2267  df-clab 2440  df-cleq 2446  df-clel 2449  df-v 3083
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