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Theorem eueq 3108
 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 2457 . . . 4
21gen2 1557 . . 3
32biantru 493 . 2
4 isset 2962 . 2
5 eqeq1 2444 . . 3
65eu4 2322 . 2
73, 4, 63bitr4i 270 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wal 1550  wex 1551   wceq 1653   wcel 1726  weu 2283  cvv 2958 This theorem is referenced by:  eueq1  3109  moeq  3112  reuhypd  4753  mptfng  5573  upxp  17660  mptfnf  24078  iotasbc  27609 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-v 2960
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