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Theorem euimmo 2066
 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 2031 . 2 (∃!𝑥𝜓 → ∃*𝑥𝜓)
2 moim 2063 . 2 (∀𝑥(𝜑𝜓) → (∃*𝑥𝜓 → ∃*𝑥𝜑))
31, 2syl5 32 1 (∀𝑥(𝜑𝜓) → (∃!𝑥𝜓 → ∃*𝑥𝜑))
 Colors of variables: wff set class Syntax hints:   → wi 4  ∀wal 1329  ∃!weu 1999  ∃*wmo 2000 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-eu 2002  df-mo 2003 This theorem is referenced by:  euim  2067  2eumo  2087  reuss2  3356
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