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Theorem 2eu2ex 2230
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 2179 . 2  |-  ( E! x E! y ph  ->  E. x E! y
ph )
2 euex 2179 . . 3  |-  ( E! y ph  ->  E. y ph )
32eximi 1566 . 2  |-  ( E. x E! y ph  ->  E. x E. y ph )
41, 3syl 15 1  |-  ( E! x E! y ph  ->  E. x E. y ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1531   E!weu 2156
This theorem is referenced by:  2eu1  2236
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160
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