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Theorem eupicka 2356
Description: Version of eupick 2355 with closed formulas. (Contributed by NM, 6-Sep-2008.)
Assertion
Ref Expression
eupicka  |-  ( ( E! x ph  /\  E. x ( ph  /\  ps ) )  ->  A. x
( ph  ->  ps )
)

Proof of Theorem eupicka
StepHypRef Expression
1 nfeu1 2296 . . 3  |-  F/ x E! x ph
2 nfe1 1845 . . 3  |-  F/ x E. x ( ph  /\  ps )
31, 2nfan 1933 . 2  |-  F/ x
( E! x ph  /\ 
E. x ( ph  /\ 
ps ) )
4 eupick 2355 . 2  |-  ( ( E! x ph  /\  E. x ( ph  /\  ps ) )  ->  ( ph  ->  ps ) )
53, 4alrimi 1882 1  |-  ( ( E! x ph  /\  E. x ( ph  /\  ps ) )  ->  A. x
( ph  ->  ps )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 367   A.wal 1396   E.wex 1617   E!weu 2284
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004
This theorem depends on definitions:  df-bi 185  df-an 369  df-ex 1618  df-nf 1622  df-eu 2288  df-mo 2289
This theorem is referenced by:  eupickbi  2358  sbiota1  31585
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