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Theorem mormo 2619
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 2046 . 2  |-  ( E* x ph  ->  E* x ( x  e.  A  /\  ph )
)
2 df-rmo 2401 . 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 1465   E*wmo 1978   E*wrmo 2396
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-sb 1721  df-eu 1980  df-mo 1981  df-rmo 2401
This theorem is referenced by:  reueq  2856  reusv1  4349
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