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Theorem mormo 2752
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 2194 . 2  |-  ( E* x ph  ->  E* x ( x  e.  A  /\  ph )
)
2 df-rmo 2551 . 2  |-  ( E* x  e.  A ph  <->  E* x ( x  e.  A  /\  ph )
)
31, 2sylibr 203 1  |-  ( E* x ph  ->  E* x  e.  A ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    e. wcel 1684   E*wmo 2144   E*wrmo 2546
This theorem is referenced by:  reueq  2962  reusv1  4534  brdom4  8155
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-rmo 2551
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