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Theorem pm5.1 831
Description: Two propositions are equivalent if they are both true. Theorem *5.1 of [WhiteheadRussell] p. 123. (Contributed by NM, 21-May-1994.)
Assertion
Ref Expression
pm5.1  |-  ( (
ph  /\  ps )  ->  ( ph  <->  ps )
)

Proof of Theorem pm5.1
StepHypRef Expression
1 pm5.501 331 . 2  |-  ( ph  ->  ( ps  <->  ( ph  <->  ps ) ) )
21biimpa 471 1  |-  ( (
ph  /\  ps )  ->  ( ph  <->  ps )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177    /\ wa 359
This theorem is referenced by:  pm5.35  870  ssconb  3467  raaan  3722  raaanv  3723  mdsymi  23897  abnotbtaxb  27793  raaan2  27862
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 178  df-an 361
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