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Theorem eueq1 3272
Description: Equality has existential uniqueness. (Contributed by NM, 5-Apr-1995.)
Hypothesis
Ref Expression
eueq1.1
Assertion
Ref Expression
eueq1
Distinct variable group:   ,

Proof of Theorem eueq1
StepHypRef Expression
1 eueq1.1 . 2
2 eueq 3271 . 2
31, 2mpbi 208 1
Colors of variables: wff setvar class
Syntax hints:  =wceq 1395  e.wcel 1818  E!weu 2282   cvv 3109
This theorem is referenced by:  eueq2  3273  eueq3  3274  fsn  6069  bj-nuliota  34586
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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