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Theorem 2eumo 2394
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 2371 . 2  |-  ( A. x ( E! y
ph  ->  E* y ph )  ->  ( E! x E* y ph  ->  E* x E! y ph )
)
2 eumo 2348 . 2  |-  ( E! y ph  ->  E* y ph )
31, 2mpg 1679 1  |-  ( E! x E* y ph  ->  E* x E! y
ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   E!weu 2319   E*wmo 2320
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-12 1950
This theorem depends on definitions:  df-bi 190  df-an 378  df-ex 1672  df-nf 1676  df-eu 2323  df-mo 2324
This theorem is referenced by: (None)
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