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Theorem pm5.21 854
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 349 . 2  |-  ( -. 
ph  ->  ( -.  ps  ->  ( ph  <->  ps )
) )
21imp 429 1  |-  ( ( -.  ph  /\  -.  ps )  ->  ( ph  <->  ps )
)
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 184    /\ wa 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 185  df-an 371
This theorem is referenced by:  nbior  856  oibabs  876  reusv7OLD  4615  onsuct0  28454  wl-nfeqfb  28537  tsbi2  29116
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