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Theorem reu6i 3290
 Description: A condition which implies existential uniqueness. (Contributed by Mario Carneiro, 2-Oct-2015.)
Assertion
Ref Expression
reu6i
Distinct variable groups:   ,   ,

Proof of Theorem reu6i
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eqeq2 2472 . . . . 5
21bibi2d 318 . . . 4
32ralbidv 2896 . . 3
43rspcev 3210 . 2
5 reu6 3288 . 2
64, 5sylibr 212 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  A.wral 2807  E.wrex 2808  E!wreu 2809 This theorem is referenced by:  eqreu  3291  riota5f  6282  negeu  9833  creur  10555  creui  10556  reuccats1  12706  lublecl  15619  dfod2  16586  lmieu  24150 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-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-reu 2814  df-v 3111
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