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Theorem 2eumo 2094
Description: Double quantification with existential uniqueness and "at most one." (Contributed by NM, 3-Dec-2001.)
Assertion
Ref Expression
2eumo  |-  ( E! x E* y ph  ->  E* x E! y
ph )

Proof of Theorem 2eumo
StepHypRef Expression
1 euimmo 2073 . 2  |-  ( A. x ( E! y
ph  ->  E* y ph )  ->  ( E! x E* y ph  ->  E* x E! y ph )
)
2 eumo 2038 . 2  |-  ( E! y ph  ->  E* y ph )
31, 2mpg 1431 1  |-  ( E! x E* y ph  ->  E* x E! y
ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E!weu 2006   E*wmo 2007
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 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515
This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743  df-eu 2009  df-mo 2010
This theorem is referenced by: (None)
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