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Theorem bi2.04 247
Description: Logical equivalence of commuted antecedents. Part of Theorem *4.87 of [WhiteheadRussell] p. 122. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
bi2.04  |-  ( (
ph  ->  ( ps  ->  ch ) )  <->  ( ps  ->  ( ph  ->  ch ) ) )

Proof of Theorem bi2.04
StepHypRef Expression
1 pm2.04 82 . 2  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  ( ps  ->  ( ph  ->  ch ) ) )
2 pm2.04 82 . 2  |-  ( ( ps  ->  ( ph  ->  ch ) )  -> 
( ph  ->  ( ps 
->  ch ) ) )
31, 2impbii 125 1  |-  ( (
ph  ->  ( ps  ->  ch ) )  <->  ( ps  ->  ( ph  ->  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  imim21b  251  pm4.87  529  imimorbdc  864  sbcom2v  1936  mor  2017  r19.21t  2482  reu8  2851  ra5  2967  unissb  3734  reusv3  4349  zfregfr  4456  tfi  4464  fun11  5158  prime  9104  raluz2  9326  isprm3  11706  isprm4  11707  bj-inf2vnlem2  13003
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