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Theorem albitr 27569
Description: Theorem *10.301 in [WhiteheadRussell] p. 151. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
albitr  |-  ( ( A. x ( ph  <->  ps )  /\  A. x
( ps  <->  ch )
)  ->  A. x
( ph  <->  ch ) )

Proof of Theorem albitr
StepHypRef Expression
1 bitr 689 . 2  |-  ( ( ( ph  <->  ps )  /\  ( ps  <->  ch )
)  ->  ( ph  <->  ch ) )
21alanimi 1551 1  |-  ( ( A. x ( ph  <->  ps )  /\  A. x
( ps  <->  ch )
)  ->  A. x
( ph  <->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358   A.wal 1529
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1535  ax-5 1546
This theorem depends on definitions:  df-bi 177  df-an 360
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