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Theorem pm5.16 865
Description: Theorem *5.16 of [WhiteheadRussell] p. 124. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 17-Oct-2013.)
Assertion
Ref Expression
pm5.16  |-  -.  (
( ph  <->  ps )  /\  ( ph 
<->  -.  ps ) )

Proof of Theorem pm5.16
StepHypRef Expression
1 pm5.18 347 . . 3  |-  ( (
ph 
<->  ps )  <->  -.  ( ph 
<->  -.  ps ) )
21biimpi 188 . 2  |-  ( (
ph 
<->  ps )  ->  -.  ( ph  <->  -.  ps )
)
3 imnan 413 . 2  |-  ( ( ( ph  <->  ps )  ->  -.  ( ph  <->  -.  ps )
)  <->  -.  ( ( ph 
<->  ps )  /\  ( ph 
<->  -.  ps ) ) )
42, 3mpbi 201 1  |-  -.  (
( ph  <->  ps )  /\  ( ph 
<->  -.  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6    <-> wb 178    /\ wa 360
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-an 362
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