MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  con1b Unicode version

Theorem con1b 323
Description: Contraposition. Bidirectional version of con1 120. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
con1b  |-  ( ( -.  ph  ->  ps )  <->  ( -.  ps  ->  ph )
)

Proof of Theorem con1b
StepHypRef Expression
1 con1 120 . 2  |-  ( ( -.  ph  ->  ps )  ->  ( -.  ps  ->  ph ) )
2 con1 120 . 2  |-  ( ( -.  ps  ->  ph )  ->  ( -.  ph  ->  ps ) )
31, 2impbii 180 1  |-  ( ( -.  ph  ->  ps )  <->  ( -.  ps  ->  ph )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176
This theorem is referenced by:  pwssun  4315  ist1-2  17091  cmpfi  17151  dchrelbas2  20492  xfree2  23041
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
  Copyright terms: Public domain W3C validator