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Theorem eqreu 3118
 Description: A condition which implies existential uniqueness. (Contributed by Mario Carneiro, 2-Oct-2015.)
Hypothesis
Ref Expression
eqreu.1
Assertion
Ref Expression
eqreu
Distinct variable groups:   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem eqreu
StepHypRef Expression
1 ralbiim 2835 . . . . 5
2 eqreu.1 . . . . . . 7
32ceqsralv 2975 . . . . . 6
43anbi2d 685 . . . . 5
51, 4syl5bb 249 . . . 4
6 reu6i 3117 . . . . 5
76ex 424 . . . 4
85, 7sylbird 227 . . 3
983impib 1151 . 2
1093com23 1159 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   w3a 936   wceq 1652   wcel 1725  wral 2697  wreu 2699 This theorem is referenced by:  uzwo3  10561  frmdup3  14803  frgpup3  15402  neiptopreu  17189  ufileu  17943 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-3an 938  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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