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Theorem 2eumo 2036
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 2015 . 2  |-  ( A. x ( E! y
ph  ->  E* y ph )  ->  ( E! x E* y ph  ->  E* x E! y ph )
)
2 eumo 1980 . 2  |-  ( E! y ph  ->  E* y ph )
31, 2mpg 1385 1  |-  ( E! x E* y ph  ->  E* x E! y
ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E!weu 1948   E*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: (None)
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