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Theorem eumo 1975
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 1947 . 2 (∃*𝑥𝜑 ↔ (∃𝑥𝜑 → ∃!𝑥𝜑))
31, 2sylibr 132 1 (∃!𝑥𝜑 → ∃*𝑥𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wex 1422  ∃!weu 1943  ∃*wmo 1944
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-mo 1947
This theorem is referenced by:  eumoi  1976  eu5  1990  euimmo  2010  moaneu  2019  eupick  2022  2eumo  2031  moeq3dc  2777  nfunsn  5259  fnoprabg  5653
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