MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  con2b Unicode version

Theorem con2b 325
Description: Contraposition. Bidirectional version of con2 110. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
con2b  |-  ( (
ph  ->  -.  ps )  <->  ( ps  ->  -.  ph )
)

Proof of Theorem con2b
StepHypRef Expression
1 con2 110 . 2  |-  ( (
ph  ->  -.  ps )  ->  ( ps  ->  -.  ph ) )
2 con2 110 . 2  |-  ( ( ps  ->  -.  ph )  ->  ( ph  ->  -.  ps ) )
31, 2impbii 181 1  |-  ( (
ph  ->  -.  ps )  <->  ( ps  ->  -.  ph )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 177
This theorem is referenced by:  mt2bi  329  pm4.15  565  nic-ax  1444  nic-axALT  1445  ssconb  3416  disjsn  3804  oneqmini  4566  kmlem4  7959  isprm3  13008  pm13.196a  27276  bnj1171  28700  bnj1176  28705  bnj1204  28712  bnj1388  28733  bnj1523  28771
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