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Theorem eupicka 2079
Description: Version of eupick 2078 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 hbeu1 2009 . . 3  |-  ( E! x ph  ->  A. x E! x ph )
2 hbe1 1471 . . 3  |-  ( E. x ( ph  /\  ps )  ->  A. x E. x ( ph  /\  ps ) )
31, 2hban 1526 . 2  |-  ( ( E! x ph  /\  E. x ( ph  /\  ps ) )  ->  A. x
( E! x ph  /\ 
E. x ( ph  /\ 
ps ) ) )
4 eupick 2078 . 2  |-  ( ( E! x ph  /\  E. x ( ph  /\  ps ) )  ->  ( ph  ->  ps ) )
53, 4alrimih 1445 1  |-  ( ( E! x ph  /\  E. x ( ph  /\  ps ) )  ->  A. x
( ph  ->  ps )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103   A.wal 1329   E.wex 1468   E!weu 1999
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515
This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-eu 2002  df-mo 2003
This theorem is referenced by:  eupickbi  2081
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