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Theorem exmo 2540
Description: Any proposition holds for some 𝑥 or holds for at most one 𝑥. (Contributed by NM, 8-Mar-1995.) Shorten proof and avoid df-eu 2567. (Revised by BJ, 14-Oct-2022.)
Assertion
Ref Expression
exmo (∃𝑥𝜑 ∨ ∃*𝑥𝜑)

Proof of Theorem exmo
StepHypRef Expression
1 nexmo 2539 . 2 (¬ ∃𝑥𝜑 → ∃*𝑥𝜑)
21orri 859 1 (∃𝑥𝜑 ∨ ∃*𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wo 844  wex 1780  ∃*wmo 2536
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970
This theorem depends on definitions:  df-bi 206  df-or 845  df-ex 1781  df-mo 2538
This theorem is referenced by:  brdom3  10386  mofal  34737
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