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Theorem pm5.501 343
Description: Theorem *5.501 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm5.501  |-  ( ph  ->  ( ps  <->  ( ph  <->  ps ) ) )

Proof of Theorem pm5.501
StepHypRef Expression
1 pm5.1im 242 . 2  |-  ( ph  ->  ( ps  ->  ( ph 
<->  ps ) ) )
2 biimp 197 . . 3  |-  ( (
ph 
<->  ps )  ->  ( ph  ->  ps ) )
32com12 32 . 2  |-  ( ph  ->  ( ( ph  <->  ps )  ->  ps ) )
41, 3impbid 194 1  |-  ( ph  ->  ( ps  <->  ( ph  <->  ps ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 188
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 189
This theorem is referenced by:  ibib  344  ibibr  345  nbn2  347  pm5.18  358  biass  361  pm5.1  869  sadadd2lem2  14436  isclo  20115  nrmmetd  21601  bj-bibibi  31182
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