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Theorem pm10.52 26959
Description: Theorem *10.52 in [WhiteheadRussell] p. 155. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
pm10.52  |-  ( E. x ph  ->  ( A. x ( ph  ->  ps )  <->  ps ) )
Distinct variable group:    ps, x
Allowed substitution hint:    ph( x)

Proof of Theorem pm10.52
StepHypRef Expression
1 19.23v 1843 . 2  |-  ( A. x ( ph  ->  ps )  <->  ( E. x ph  ->  ps ) )
2 pm5.5 328 . 2  |-  ( E. x ph  ->  (
( E. x ph  ->  ps )  <->  ps )
)
31, 2syl5bb 250 1  |-  ( E. x ph  ->  ( A. x ( ph  ->  ps )  <->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178   A.wal 1532   E.wex 1533
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1538  ax-5 1549  ax-17 1608  ax-9 1641  ax-8 1648  ax-6 1707  ax-11 1719
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1534  df-nf 1537
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