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Theorem con4bii 303
Description: A contraposition inference. (Contributed by NM, 21-May-1994.)
Hypothesis
Ref Expression
con4bii.1  |-  ( -. 
ph 
<->  -.  ps )
Assertion
Ref Expression
con4bii  |-  ( ph  <->  ps )

Proof of Theorem con4bii
StepHypRef Expression
1 con4bii.1 . 2  |-  ( -. 
ph 
<->  -.  ps )
2 notbi 301 . 2  |-  ( (
ph 
<->  ps )  <->  ( -.  ph  <->  -. 
ps ) )
31, 2mpbir 214 1  |-  ( ph  <->  ps )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 189
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 190
This theorem is referenced by:  2false  356  2ralor  2971  gencbval  3105  eq0  3758  snnzb  4048  raldifsnb  4115  uni0b  4236  ceqsralv2  30406  tsna1  32430
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