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Theorem reurmo 2524
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 2522 . 2  |-  ( E! x  e.  A  ph  <->  ( E. x  e.  A  ph 
/\  E* x  e.  A  ph ) )
21simprbi 260 1  |-  ( E! x  e.  A  ph  ->  E* x  e.  A  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wrex 2307   E!wreu 2308   E*wrmo 2309
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428
This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904  df-rex 2312  df-reu 2313  df-rmo 2314
This theorem is referenced by: (None)
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