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Theorem pm4.14 580
Description: Theorem *4.14 of [WhiteheadRussell] p. 117. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 23-Oct-2012.)
Assertion
Ref Expression
pm4.14  |-  ( ( ( ph  /\  ps )  ->  ch )  <->  ( ( ph  /\  -.  ch )  ->  -.  ps ) )

Proof of Theorem pm4.14
StepHypRef Expression
1 con34b 293 . . 3  |-  ( ( ps  ->  ch )  <->  ( -.  ch  ->  -.  ps ) )
21imbi2i 313 . 2  |-  ( (
ph  ->  ( ps  ->  ch ) )  <->  ( ph  ->  ( -.  ch  ->  -. 
ps ) ) )
3 impexp 447 . 2  |-  ( ( ( ph  /\  ps )  ->  ch )  <->  ( ph  ->  ( ps  ->  ch ) ) )
4 impexp 447 . 2  |-  ( ( ( ph  /\  -.  ch )  ->  -.  ps ) 
<->  ( ph  ->  ( -.  ch  ->  -.  ps )
) )
52, 3, 43bitr4i 280 1  |-  ( ( ( ph  /\  ps )  ->  ch )  <->  ( ( ph  /\  -.  ch )  ->  -.  ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 187    /\ wa 370
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 188  df-an 372
This theorem is referenced by:  pm3.37  581  ndvdssub  14375
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