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Theorem reurmo 2768
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 2766 . 2  |-  ( E! x  e.  A  ph  <->  ( E. x  e.  A  ph 
/\  E* x  e.  A ph ) )
21simprbi 450 1  |-  ( E! x  e.  A  ph  ->  E* x  e.  A ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wrex 2557   E!wreu 2558   E*wrmo 2559
This theorem is referenced by:  reuxfrd  4575  0frgp  15104  reuxfr4d  23155  reuimrmo  28059  2reurmo  28063  2rexreu  28066  2reu2  28068
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-rex 2562  df-reu 2563  df-rmo 2564
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