MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm5.21 Unicode version

Theorem pm5.21 831
Description: Two propositions are equivalent if they are both false. Theorem *5.21 of [WhiteheadRussell] p. 124. (Contributed by NM, 21-May-1994.)
Assertion
Ref Expression
pm5.21  |-  ( ( -.  ph  /\  -.  ps )  ->  ( ph  <->  ps )
)

Proof of Theorem pm5.21
StepHypRef Expression
1 pm5.21im 338 . 2  |-  ( -. 
ph  ->  ( -.  ps  ->  ( ph  <->  ps )
) )
21imp 418 1  |-  ( ( -.  ph  /\  -.  ps )  ->  ( ph  <->  ps )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176    /\ wa 358
This theorem is referenced by:  oibabs  851  reusv7OLD  4562  onsuct0  24952
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  df-an 360
  Copyright terms: Public domain W3C validator