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Theorem 2eu2ex 2355
Description: Double existential uniqueness. (Contributed by NM, 3-Dec-2001.)
Assertion
Ref Expression
2eu2ex  |-  ( E! x E! y ph  ->  E. x E. y ph )

Proof of Theorem 2eu2ex
StepHypRef Expression
1 euex 2304 . 2  |-  ( E! x E! y ph  ->  E. x E! y
ph )
2 euex 2304 . . 3  |-  ( E! y ph  ->  E. y ph )
32eximi 1585 . 2  |-  ( E. x E! y ph  ->  E. x E. y ph )
41, 3syl 16 1  |-  ( E! x E! y ph  ->  E. x E. y ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1550   E!weu 2281
This theorem is referenced by:  2eu1  2361
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285
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