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Theorem exmo 2523
Description: Something exists or at most one exists. (Contributed by NM, 8-Mar-1995.)
Assertion
Ref Expression
exmo (∃𝑥𝜑 ∨ ∃*𝑥𝜑)

Proof of Theorem exmo
StepHypRef Expression
1 pm2.21 120 . . 3 (¬ ∃𝑥𝜑 → (∃𝑥𝜑 → ∃!𝑥𝜑))
2 df-mo 2503 . . 3 (∃*𝑥𝜑 ↔ (∃𝑥𝜑 → ∃!𝑥𝜑))
31, 2sylibr 224 . 2 (¬ ∃𝑥𝜑 → ∃*𝑥𝜑)
43orri 390 1 (∃𝑥𝜑 ∨ ∃*𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 382  wex 1744  ∃!weu 2498  ∃*wmo 2499
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-or 384  df-mo 2503
This theorem is referenced by:  exmoeu  2531  moanim  2558  moexex  2570  mo2icl  3418  mosubopt  5001  dff3  6412  brdom3  9388  mof  32534
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