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Theorem eupicka 2220
Description: Version of eupick 2219 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 2166 . . 3  |-  F/ x E! x ph
2 nfe1 1718 . . 3  |-  F/ x E. x ( ph  /\  ps )
31, 2nfan 1783 . 2  |-  F/ x
( E! x ph  /\ 
E. x ( ph  /\ 
ps ) )
4 eupick 2219 . 2  |-  ( ( E! x ph  /\  E. x ( ph  /\  ps ) )  ->  ( ph  ->  ps ) )
53, 4alrimi 1757 1  |-  ( ( E! x ph  /\  E. x ( ph  /\  ps ) )  ->  A. x
( ph  ->  ps )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   A.wal 1530   E.wex 1531   E!weu 2156
This theorem is referenced by:  eupickbi  2222  isconcl7a  26208  sbiota1  27737
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  df-mo 2161
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