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Theorem 2eumo 2216
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 2192 . 2  |-  ( A. x ( E! y
ph  ->  E* y ph )  ->  ( E! x E* y ph  ->  E* x E! y ph )
)
2 eumo 2183 . 2  |-  ( E! y ph  ->  E* y ph )
31, 2mpg 1535 1  |-  ( E! x E* y ph  ->  E* x E! y
ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E!weu 2143   E*wmo 2144
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148
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