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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  531  imimorbdc  866  sbcom2v  1938  mor  2019  r19.21t  2484  reu8  2853  ra5  2969  unissb  3736  reusv3  4351  zfregfr  4458  tfi  4466  fun11  5160  prime  9118  raluz2  9342  isprm3  11726  isprm4  11727  bj-inf2vnlem2  13096
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