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Theorem 2eumo 2367
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 2343 . 2  |-  ( A. x ( E! y
ph  ->  E* y ph )  ->  ( E! x E* y ph  ->  E* x E! y ph )
)
2 eumo 2314 . 2  |-  ( E! y ph  ->  E* y ph )
31, 2mpg 1621 1  |-  ( E! x E* y ph  ->  E* x E! y
ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   E!weu 2283   E*wmo 2284
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-12 1855
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1614  df-nf 1618  df-eu 2287  df-mo 2288
This theorem is referenced by: (None)
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