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Theorem pm10.52 36399
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 1807 . 2  |-  ( A. x ( ph  ->  ps )  <->  ( E. x ph  ->  ps ) )
2 pm5.5 337 . 2  |-  ( E. x ph  ->  (
( E. x ph  ->  ps )  <->  ps )
)
31, 2syl5bb 260 1  |-  ( E. x ph  ->  ( A. x ( ph  ->  ps )  <->  ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 187   A.wal 1435   E.wex 1659
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794
This theorem depends on definitions:  df-bi 188  df-ex 1660
This theorem is referenced by: (None)
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