MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  eumoi Structured version   Visualization version   GIF version

Theorem eumoi 2630
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 2628 . 2 (∃!𝑥𝜑 → ∃*𝑥𝜑)
31, 2ax-mp 5 1 ∃*𝑥𝜑
Colors of variables: wff setvar class
Syntax hints:  ∃!weu 2599  ∃*wmo 2600
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-mo 2604
This theorem is referenced by:  euxfr  3525
  Copyright terms: Public domain W3C validator