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Theorem exmoeu2 2074
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 2073 . 2 (∃!𝑥𝜑 ↔ (∃𝑥𝜑 ∧ ∃*𝑥𝜑))
21baibr 920 1 (∃𝑥𝜑 → (∃*𝑥𝜑 ↔ ∃!𝑥𝜑))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 105  wex 1492  ∃!weu 2026  ∃*wmo 2027
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535
This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-eu 2029  df-mo 2030
This theorem is referenced by:  n0mmoeu  3439  fneu  5316
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