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Theorem pm4.15 583
Description: Theorem *4.15 of [WhiteheadRussell] p. 117. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 18-Nov-2012.)
Assertion
Ref Expression
pm4.15  |-  ( ( ( ph  /\  ps )  ->  -.  ch )  <->  ( ( ps  /\  ch )  ->  -.  ph ) )

Proof of Theorem pm4.15
StepHypRef Expression
1 con2b 335 . 2  |-  ( ( ( ps  /\  ch )  ->  -.  ph )  <->  ( ph  ->  -.  ( ps  /\  ch ) ) )
2 nan 582 . 2  |-  ( (
ph  ->  -.  ( ps  /\ 
ch ) )  <->  ( ( ph  /\  ps )  ->  -.  ch ) )
31, 2bitr2i 253 1  |-  ( ( ( ph  /\  ps )  ->  -.  ch )  <->  ( ( ps  /\  ch )  ->  -.  ph ) )
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: (None)
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