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Theorem eumo 2279
Description: Existential uniqueness implies "at most one." (Contributed by NM, 23-Mar-1995.)
Assertion
Ref Expression
eumo  |-  ( E! x ph  ->  E* x ph )

Proof of Theorem eumo
StepHypRef Expression
1 eu5 2277 . 2  |-  ( E! x ph  <->  ( E. x ph  /\  E* x ph ) )
21simprbi 451 1  |-  ( E! x ph  ->  E* x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1547   E!weu 2239   E*wmo 2240
This theorem is referenced by:  eumoi  2280  euimmo  2288  moaneu  2298  eupick  2302  2eumo  2312  2exeu  2316  2eu2  2320  2eu5  2323  moeq3  3055  euabex  4366  nfunsn  5702  dff3  5822  zfrep6  5908  fnoprabg  6111  nqerf  8741  uptx  17579  txcn  17580  f1otrspeq  27060  pm14.12  27291
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2243  df-mo 2244
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