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Theorem notbi 288
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 21 . . 3  |-  ( (
ph 
<->  ps )  ->  ( ph 
<->  ps ) )
21notbid 287 . 2  |-  ( (
ph 
<->  ps )  ->  ( -.  ph  <->  -.  ps )
)
3 id 21 . . 3  |-  ( ( -.  ph  <->  -.  ps )  ->  ( -.  ph  <->  -.  ps )
)
43con4bid 286 . 2  |-  ( ( -.  ph  <->  -.  ps )  ->  ( ph  <->  ps )
)
52, 4impbii 182 1  |-  ( (
ph 
<->  ps )  <->  ( -.  ph  <->  -. 
ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 5    <-> wb 178
This theorem is referenced by:  notbii  289  con4bii  290  con2bi  320  nbn2  336  pm5.32  619  cbvexd  1954  isocnv3  5790  symdifass  23779  onsuct0  24287  f1omvdco3  26791  bothfbothsame  27247  aisbnaxb  27258
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
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