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Theorem euimmo 2015
Description: Uniqueness implies "at most one" through implication. (Contributed by NM, 22-Apr-1995.)
Assertion
Ref Expression
euimmo (∀𝑥(𝜑𝜓) → (∃!𝑥𝜓 → ∃*𝑥𝜑))

Proof of Theorem euimmo
StepHypRef Expression
1 eumo 1980 . 2 (∃!𝑥𝜓 → ∃*𝑥𝜓)
2 moim 2012 . 2 (∀𝑥(𝜑𝜓) → (∃*𝑥𝜓 → ∃*𝑥𝜑))
31, 2syl5 32 1 (∀𝑥(𝜑𝜓) → (∃!𝑥𝜓 → ∃*𝑥𝜑))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1287  ∃!weu 1948  ∃*wmo 1949
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-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-eu 1951  df-mo 1952
This theorem is referenced by:  euim  2016  2eumo  2036  reuss2  3279
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