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

Theorem biortn 407
Description: A wff is equivalent to its negated disjunction with falsehood. (Contributed by NM, 9-Jul-2012.)
Assertion
Ref Expression
biortn  |-  ( ph  ->  ( ps  <->  ( -.  ph  \/  ps ) ) )

Proof of Theorem biortn
StepHypRef Expression
1 notnot1 125 . 2  |-  ( ph  ->  -.  -.  ph )
2 biorf 406 . 2  |-  ( -. 
-.  ph  ->  ( ps  <->  ( -.  ph  \/  ps ) ) )
31, 2syl 17 1  |-  ( ph  ->  ( ps  <->  ( -.  ph  \/  ps ) ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 187    \/ wo 369
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 188  df-or 371
This theorem is referenced by:  oranabs  864  xrdifh  28198  ballotlemfc0  29151  ballotlemfcc  29152  topdifinfindis  31483  topdifinffinlem  31484  4atlem3a  32871  4atlem3b  32872
  Copyright terms: Public domain W3C validator