ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  exmoeu2 GIF version

Theorem exmoeu2 2003
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 2002 . 2 (∃!𝑥𝜑 ↔ (∃𝑥𝜑 ∧ ∃*𝑥𝜑))
21baibr 870 1 (∃𝑥𝜑 → (∃*𝑥𝜑 ↔ ∃!𝑥𝜑))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 104  wex 1433  ∃!weu 1955  ∃*wmo 1956
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480
This theorem depends on definitions:  df-bi 116  df-nf 1402  df-sb 1700  df-eu 1958  df-mo 1959
This theorem is referenced by:  n0mmoeu  3318  fneu  5152
  Copyright terms: Public domain W3C validator