MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  eupicka Unicode version

Theorem eupicka 2207
Description: Version of eupick 2206 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 2153 . . 3  |-  F/ x E! x ph
2 nfe1 1706 . . 3  |-  F/ x E. x ( ph  /\  ps )
31, 2nfan 1771 . 2  |-  F/ x
( E! x ph  /\ 
E. x ( ph  /\ 
ps ) )
4 eupick 2206 . 2  |-  ( ( E! x ph  /\  E. x ( ph  /\  ps ) )  ->  ( ph  ->  ps ) )
53, 4alrimi 1745 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 1527   E.wex 1528   E!weu 2143
This theorem is referenced by:  eupickbi  2209  isconcl7a  26105  sbiota1  27634
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148
  Copyright terms: Public domain W3C validator