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Theorem mormo 2922
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 2334 . 2  |-  ( E* x ph  ->  E* x ( x  e.  A  /\  ph )
)
2 df-rmo 2715 . 2  |-  ( E* x  e.  A ph  <->  E* x ( x  e.  A  /\  ph )
)
31, 2sylibr 205 1  |-  ( E* x ph  ->  E* x  e.  A ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360    e. wcel 1726   E*wmo 2284   E*wrmo 2710
This theorem is referenced by:  reueq  3133  reusv1  4725  brdom4  8410
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-rmo 2715
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