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Theorem reurmo 2755
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 2753 . 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 2544   E!wreu 2545   E*wrmo 2546
This theorem is referenced by:  reuxfrd  4559  0frgp  15088  reuxfr4d  23139  reuimrmo  27956  2reurmo  27960  2rexreu  27963  2reu2  27965
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-rex 2549  df-reu 2550  df-rmo 2551
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