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Theorem mormo 2642
Description: Unrestricted "at most one" implies restricted "at most one". (Contributed by NM, 16-Jun-2017.)
Assertion
Ref Expression
mormo  |-  ( E* x ph  ->  E* x  e.  A  ph )

Proof of Theorem mormo
StepHypRef Expression
1 moan 2068 . 2  |-  ( E* x ph  ->  E* x ( x  e.  A  /\  ph )
)
2 df-rmo 2424 . 2  |-  ( E* x  e.  A  ph  <->  E* x ( x  e.  A  /\  ph )
)
31, 2sylibr 133 1  |-  ( E* x ph  ->  E* x  e.  A  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    e. wcel 1480   E*wmo 2000   E*wrmo 2419
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515
This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-eu 2002  df-mo 2003  df-rmo 2424
This theorem is referenced by:  reueq  2883  reusv1  4379
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