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Theorem eumo 1929
Description: Existential uniqueness implies "at most one." (Contributed by NM, 23-Mar-1995.) (Proof rewritten by Jim Kingdon, 27-May-2018.)
Assertion
Ref Expression
eumo (∃!xφ∃*xφ)

Proof of Theorem eumo
StepHypRef Expression
1 ax-1 5 . 2 (∃!xφ → (xφ∃!xφ))
2 df-mo 1901 . 2 (∃*xφ ↔ (xφ∃!xφ))
31, 2sylibr 137 1 (∃!xφ∃*xφ)
Colors of variables: wff set class
Syntax hints:  wi 4  wex 1378  ∃!weu 1897  ∃*wmo 1898
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110  df-mo 1901
This theorem is referenced by:  eumoi  1930  eu5  1944  euimmo  1964  moaneu  1973  eupick  1976  2eumo  1985  moeq3dc  2711  nfunsn  5150  fnoprabg  5544
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