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Theorem mon 1974
Description: There is at most one of something which does not exist. (Contributed by Jim Kingdon, 5-Jul-2018.)
Assertion
Ref Expression
mon (¬ ∃𝑥𝜑 → ∃*𝑥𝜑)

Proof of Theorem mon
StepHypRef Expression
1 ax-in2 578 . 2 (¬ ∃𝑥𝜑 → (∃𝑥𝜑 → ∃!𝑥𝜑))
2 df-mo 1949 . 2 (∃*𝑥𝜑 ↔ (∃𝑥𝜑 → ∃!𝑥𝜑))
31, 2sylibr 132 1 (¬ ∃𝑥𝜑 → ∃*𝑥𝜑)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wex 1424  ∃!weu 1945  ∃*wmo 1946
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in2 578
This theorem depends on definitions:  df-bi 115  df-mo 1949
This theorem is referenced by:  moexexdc  2029
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