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Theorem reu6i 3117
 Description: A condition which implies existential uniqueness. (Contributed by Mario Carneiro, 2-Oct-2015.)
Assertion
Ref Expression
reu6i
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem reu6i
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eqeq2 2444 . . . . 5
21bibi2d 310 . . . 4
32ralbidv 2717 . . 3
43rspcev 3044 . 2
5 reu6 3115 . 2
64, 5sylibr 204 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wceq 1652   wcel 1725  wral 2697  wrex 2698  wreu 2699 This theorem is referenced by:  eqreu  3118  riota5f  6566  negeu  9286  creur  9984  creui  9985  dfod2  15190 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-reu 2704  df-v 2950
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