MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  dfor2 Unicode version

Theorem dfor2 402
Description: Logical 'or' expressed in terms of implication only. Theorem *5.25 of [WhiteheadRussell] p. 124. (Contributed by NM, 12-Aug-2004.) (Proof shortened by Wolf Lammen, 20-Oct-2012.)
Assertion
Ref Expression
dfor2  |-  ( (
ph  \/  ps )  <->  ( ( ph  ->  ps )  ->  ps ) )

Proof of Theorem dfor2
StepHypRef Expression
1 pm2.62 400 . 2  |-  ( (
ph  \/  ps )  ->  ( ( ph  ->  ps )  ->  ps )
)
2 pm2.68 401 . 2  |-  ( ( ( ph  ->  ps )  ->  ps )  -> 
( ph  \/  ps ) )
31, 2impbii 182 1  |-  ( (
ph  \/  ps )  <->  ( ( ph  ->  ps )  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178    \/ wo 359
This theorem is referenced by:  imimorb  852
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-or 361
  Copyright terms: Public domain W3C validator