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Theorem eupicka 2093
Description: Version of eupick 2092 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 2023 . . 3  |-  ( E! x ph  ->  A. x E! x ph )
2 hbe1 1482 . . 3  |-  ( E. x ( ph  /\  ps )  ->  A. x E. x ( ph  /\  ps ) )
31, 2hban 1534 . 2  |-  ( ( E! x ph  /\  E. x ( ph  /\  ps ) )  ->  A. x
( E! x ph  /\ 
E. x ( ph  /\ 
ps ) ) )
4 eupick 2092 . 2  |-  ( ( E! x ph  /\  E. x ( ph  /\  ps ) )  ->  ( ph  ->  ps ) )
53, 4alrimih 1456 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 1340   E.wex 1479   E!weu 2013
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 699  ax-5 1434  ax-7 1435  ax-gen 1436  ax-ie1 1480  ax-ie2 1481  ax-8 1491  ax-10 1492  ax-11 1493  ax-i12 1494  ax-bndl 1496  ax-4 1497  ax-17 1513  ax-i9 1517  ax-ial 1521  ax-i5r 1522
This theorem depends on definitions:  df-bi 116  df-nf 1448  df-sb 1750  df-eu 2016  df-mo 2017
This theorem is referenced by:  eupickbi  2095
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