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Theorem eqreu 3205
 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 2899 . . . . 5
2 eqreu.1 . . . . . . 7
32ceqsralv 3052 . . . . . 6
43anbi2d 708 . . . . 5
51, 4syl5bb 260 . . . 4
6 reu6i 3204 . . . . 5
76ex 435 . . . 4
85, 7sylbird 238 . . 3
983impib 1203 . 2
1093com23 1211 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370   w3a 982   wceq 1437   wcel 1872  wral 2714  wreu 2716 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2063  ax-ext 2408 This theorem depends on definitions:  df-bi 188  df-an 372  df-3an 984  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-eu 2280  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2558  df-ral 2719  df-rex 2720  df-reu 2721  df-v 3024 This theorem is referenced by:  uzwo3  11210  frmdup3  16594  frgpup3  17371  neiptopreu  20091  ufileu  20876  mirreu  24651  lmireu  24774  symgfcoeu  28560
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