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Theorem pm5.16 860
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 pm5.18 345 . . 3  |-  ( (
ph 
<->  ps )  <->  -.  ( ph 
<->  -.  ps ) )
21biimpi 186 . 2  |-  ( (
ph 
<->  ps )  ->  -.  ( ph  <->  -.  ps )
)
3 imnan 411 . 2  |-  ( ( ( ph  <->  ps )  ->  -.  ( ph  <->  -.  ps )
)  <->  -.  ( ( ph 
<->  ps )  /\  ( ph 
<->  -.  ps ) ) )
42, 3mpbi 199 1  |-  -.  (
( ph  <->  ps )  /\  ( ph 
<->  -.  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176    /\ wa 358
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
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