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Theorem moeuex 2668
Description: Uniqueness implies that existence is equivalent to unique existence. (Contributed by BJ, 7-Oct-2022.)
Assertion
Ref Expression
moeuex (∃*𝑥𝜑 → (∃𝑥𝜑 ↔ ∃!𝑥𝜑))

Proof of Theorem moeuex
StepHypRef Expression
1 df-eu 2655 . 2 (∃!𝑥𝜑 ↔ (∃𝑥𝜑 ∧ ∃*𝑥𝜑))
21rbaibr 541 1 (∃*𝑥𝜑 → (∃𝑥𝜑 ↔ ∃!𝑥𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 209  wex 1781  ∃*wmo 2622  ∃!weu 2654
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 210  df-an 400  df-eu 2655
This theorem is referenced by: (None)
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