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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  552  imimorbdc  891  sbcom2v  1978  mor  2061  r19.21t  2545  reu8  2926  ra5  3043  unissb  3826  reusv3  4445  zfregfr  4558  tfi  4566  fun11  5265  prime  9311  raluz2  9538  isprm3  12072  isprm4  12073  bj-inf2vnlem2  14006
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