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Theorem nexmo1 36386
Description: If there is no case where wff is true, it is true for at most one case. (Contributed by Peter Mazsa, 27-Sep-2021.)
Assertion
Ref Expression
nexmo1 (¬ ∃𝑥𝜑 → ∃*𝑥𝜑)

Proof of Theorem nexmo1
StepHypRef Expression
1 pm2.21 123 . 2 (¬ ∃𝑥𝜑 → (∃𝑥𝜑 → ∃!𝑥𝜑))
2 moeu 2583 . 2 (∃*𝑥𝜑 ↔ (∃𝑥𝜑 → ∃!𝑥𝜑))
31, 2sylibr 233 1 (¬ ∃𝑥𝜑 → ∃*𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wex 1782  ∃*wmo 2538  ∃!weu 2568
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971
This theorem depends on definitions:  df-bi 206  df-an 397  df-ex 1783  df-mo 2540  df-eu 2569
This theorem is referenced by: (None)
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