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Theorem pm5.1 830
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 pm5.501 330 . 2  |-  ( ph  ->  ( ps  <->  ( ph  <->  ps ) ) )
21biimpa 470 1  |-  ( (
ph  /\  ps )  ->  ( ph  <->  ps )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358
This theorem is referenced by:  pm5.35  869  ssconb  3309  raaan  3561  raaanv  3562  mdsymi  22991  bothtbothsame  27867  bothfbothsame  27868  abnotbtaxb  27884  raaan2  27953
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
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