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Theorem exmoeu2 2598
Description: Existence implies "at most one" is equivalent to uniqueness. (Contributed by NM, 5-Apr-2004.)
Assertion
Ref Expression
exmoeu2 (∃𝑥𝜑 → (∃*𝑥𝜑 ↔ ∃!𝑥𝜑))

Proof of Theorem exmoeu2
StepHypRef Expression
1 eu5 2597 . 2 (∃!𝑥𝜑 ↔ (∃𝑥𝜑 ∧ ∃*𝑥𝜑))
21baibr 983 1 (∃𝑥𝜑 → (∃*𝑥𝜑 ↔ ∃!𝑥𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wex 1817  ∃!weu 2571  ∃*wmo 2572
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1835  ax-4 1850  ax-5 1952  ax-6 2018
This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1818  df-eu 2575  df-mo 2576
This theorem is referenced by:  fneu  6108
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