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Theorem eumo 2196
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 2194 . 2  |-  ( E! x ph  <->  ( E. x ph  /\  E* x ph ) )
21simprbi 450 1  |-  ( E! x ph  ->  E* x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1531   E!weu 2156   E*wmo 2157
This theorem is referenced by:  eumoi  2197  euimmo  2205  moaneu  2215  eupick  2219  2eumo  2229  2exeu  2233  2eu2  2237  2eu5  2240  moeq3  2955  euabex  4250  nfunsn  5574  dff3  5689  zfrep6  5764  fnoprabg  5961  nqerf  8570  uptx  17335  txcn  17336  f1otrspeq  27493  pm14.12  27724
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161
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