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Theorem notbi 287
Description: Contraposition. Theorem *4.11 of [WhiteheadRussell] p. 117. (Contributed by NM, 21-May-1994.) (Proof shortened by Wolf Lammen, 12-Jun-2013.)
Assertion
Ref Expression
notbi  |-  ( (
ph 
<->  ps )  <->  ( -.  ph  <->  -. 
ps ) )

Proof of Theorem notbi
StepHypRef Expression
1 id 20 . . 3  |-  ( (
ph 
<->  ps )  ->  ( ph 
<->  ps ) )
21notbid 286 . 2  |-  ( (
ph 
<->  ps )  ->  ( -.  ph  <->  -.  ps )
)
3 id 20 . . 3  |-  ( ( -.  ph  <->  -.  ps )  ->  ( -.  ph  <->  -.  ps )
)
43con4bid 285 . 2  |-  ( ( -.  ph  <->  -.  ps )  ->  ( ph  <->  ps )
)
52, 4impbii 181 1  |-  ( (
ph 
<->  ps )  <->  ( -.  ph  <->  -. 
ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 177
This theorem is referenced by:  notbii  288  con4bii  289  con2bi  319  nbn2  335  pm5.32  618  cbvexd  2059  isocnv3  6011  symdifass  25585  onsuct0  26095  f1omvdco3  27260  cbvexdOLD7  29419
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 178
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