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Theorem eumoi 2498
Description: "At most one" inferred from existential uniqueness. (Contributed by NM, 5-Apr-1995.)
Hypothesis
Ref Expression
eumoi.1 ∃!𝑥𝜑
Assertion
Ref Expression
eumoi ∃*𝑥𝜑

Proof of Theorem eumoi
StepHypRef Expression
1 eumoi.1 . 2 ∃!𝑥𝜑
2 eumo 2497 . 2 (∃!𝑥𝜑 → ∃*𝑥𝜑)
31, 2ax-mp 5 1 ∃*𝑥𝜑
Colors of variables: wff setvar class
Syntax hints:  ∃!weu 2468  ∃*wmo 2469
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886
This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1703  df-eu 2472  df-mo 2473
This theorem is referenced by:  euxfr  3386
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