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Theorem pm10.52 36714
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 1818 . 2  |-  ( A. x ( ph  ->  ps )  <->  ( E. x ph  ->  ps ) )
2 pm5.5 338 . 2  |-  ( E. x ph  ->  (
( E. x ph  ->  ps )  <->  ps )
)
31, 2syl5bb 261 1  |-  ( E. x ph  ->  ( A. x ( ph  ->  ps )  <->  ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 188   A.wal 1442   E.wex 1663
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805
This theorem depends on definitions:  df-bi 189  df-ex 1664
This theorem is referenced by: (None)
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