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Theorem pm10.52 27663
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 1844 . 2  |-  ( A. x ( ph  ->  ps )  <->  ( E. x ph  ->  ps ) )
2 pm5.5 326 . 2  |-  ( E. x ph  ->  (
( E. x ph  ->  ps )  <->  ps )
)
31, 2syl5bb 248 1  |-  ( E. x ph  ->  ( A. x ( ph  ->  ps )  <->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   A.wal 1530   E.wex 1531
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-nf 1535
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