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Theorem 2eumo 2085
 Description: Double quantification with existential uniqueness and "at most one." (Contributed by NM, 3-Dec-2001.)
Assertion
Ref Expression
2eumo (∃!𝑥∃*𝑦𝜑 → ∃*𝑥∃!𝑦𝜑)

Proof of Theorem 2eumo
StepHypRef Expression
1 euimmo 2064 . 2 (∀𝑥(∃!𝑦𝜑 → ∃*𝑦𝜑) → (∃!𝑥∃*𝑦𝜑 → ∃*𝑥∃!𝑦𝜑))
2 eumo 2029 . 2 (∃!𝑦𝜑 → ∃*𝑦𝜑)
31, 2mpg 1427 1 (∃!𝑥∃*𝑦𝜑 → ∃*𝑥∃!𝑦𝜑)
 Colors of variables: wff set class Syntax hints:   → wi 4  ∃!weu 1997  ∃*wmo 1998 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 2000  df-mo 2001 This theorem is referenced by: (None)
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