MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  con4bii Unicode version

Theorem con4bii 289
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 287 . 2  |-  ( (
ph 
<->  ps )  <->  ( -.  ph  <->  -. 
ps ) )
31, 2mpbir 201 1  |-  ( ph  <->  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 177
This theorem is referenced by:  2false  340  19.35  1607  2ralor  2820  gencbval  2943  eq0  3585  uni0b  3982  nbusgra  21306
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
  Copyright terms: Public domain W3C validator