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Theorem con2bi 318
Description: Contraposition. Theorem *4.12 of [WhiteheadRussell] p. 117. (Contributed by NM, 15-Apr-1995.) (Proof shortened by Wolf Lammen, 3-Jan-2013.)
Assertion
Ref Expression
con2bi  |-  ( (
ph 
<->  -.  ps )  <->  ( ps  <->  -. 
ph ) )

Proof of Theorem con2bi
StepHypRef Expression
1 notbi 286 . 2  |-  ( (
ph 
<->  -.  ps )  <->  ( -.  ph  <->  -. 
-.  ps ) )
2 notnot 282 . . 3  |-  ( ps  <->  -. 
-.  ps )
32bibi2i 304 . 2  |-  ( ( -.  ph  <->  ps )  <->  ( -.  ph  <->  -. 
-.  ps ) )
4 bicom 191 . 2  |-  ( ( -.  ph  <->  ps )  <->  ( ps  <->  -. 
ph ) )
51, 3, 43bitr2i 264 1  |-  ( (
ph 
<->  -.  ps )  <->  ( ps  <->  -. 
ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176
This theorem is referenced by:  con2bid  319  nbbn  347
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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