MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  3oran Structured version   Unicode version

Theorem 3oran 992
Description: Triple disjunction in terms of triple conjunction. (Contributed by NM, 8-Oct-2012.)
Assertion
Ref Expression
3oran  |-  ( (
ph  \/  ps  \/  ch )  <->  -.  ( -.  ph 
/\  -.  ps  /\  -.  ch ) )

Proof of Theorem 3oran
StepHypRef Expression
1 3ioran 991 . . 3  |-  ( -.  ( ph  \/  ps  \/  ch )  <->  ( -.  ph 
/\  -.  ps  /\  -.  ch ) )
21con1bii 331 . 2  |-  ( -.  ( -.  ph  /\  -.  ps  /\  -.  ch ) 
<->  ( ph  \/  ps  \/  ch ) )
32bicomi 202 1  |-  ( (
ph  \/  ps  \/  ch )  <->  -.  ( -.  ph 
/\  -.  ps  /\  -.  ch ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184    \/ w3o 972    /\ w3a 973
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 185  df-or 370  df-an 371  df-3or 974  df-3an 975
This theorem is referenced by:  dalawlem10  34694
  Copyright terms: Public domain W3C validator