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Theorem notbi 286
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 19 . . 3  |-  ( (
ph 
<->  ps )  ->  ( ph 
<->  ps ) )
21notbid 285 . 2  |-  ( (
ph 
<->  ps )  ->  ( -.  ph  <->  -.  ps )
)
3 id 19 . . 3  |-  ( ( -.  ph  <->  -.  ps )  ->  ( -.  ph  <->  -.  ps )
)
43con4bid 284 . 2  |-  ( ( -.  ph  <->  -.  ps )  ->  ( ph  <->  ps )
)
52, 4impbii 180 1  |-  ( (
ph 
<->  ps )  <->  ( -.  ph  <->  -. 
ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176
This theorem is referenced by:  notbii  287  con4bii  288  con2bi  318  nbn2  334  pm5.32  617  cbvexd  1949  isocnv3  5829  symdifass  24371  onsuct0  24880  f1omvdco3  27392  bothfbothsame  27868  aisbnaxb  27879
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
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