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Theorem reurmo 3044
Description: Restricted existential uniqueness implies restricted "at most one." (Contributed by NM, 16-Jun-2017.)
Assertion
Ref Expression
reurmo  |-  ( E! x  e.  A  ph  ->  E* x  e.  A  ph )

Proof of Theorem reurmo
StepHypRef Expression
1 reu5 3042 . 2  |-  ( E! x  e.  A  ph  <->  ( E. x  e.  A  ph 
/\  E* x  e.  A  ph ) )
21simprbi 464 1  |-  ( E! x  e.  A  ph  ->  E* x  e.  A  ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   E.wrex 2800   E!wreu 2801   E*wrmo 2802
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588  df-eu 2266  df-mo 2267  df-rex 2805  df-reu 2806  df-rmo 2807
This theorem is referenced by:  reuxfrd  4628  enqeq  9217  eqsqrd  12976  efgred2  16374  0frgp  16400  frgpnabllem2  16476  frgpcyg  18134  qtophmeo  19525  lmieu  23276  reuxfr4d  26046  reuimrmo  30170  2reurmo  30174  2rexreu  30177  2reu2  30179
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