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Theorem pm5.1 832
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 pm5.501 332 . 2  |-  ( ph  ->  ( ps  <->  ( ph  <->  ps ) ) )
21biimpa 472 1  |-  ( (
ph  /\  ps )  ->  ( ph  <->  ps )
)
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178    /\ wa 360
This theorem is referenced by:  pm5.35  871  ssconb  3310  raaan  3562  raaanv  3563  mdsymi  22983  bothtbothsame  27246  bothfbothsame  27247  abnotbtaxb  27263  raaan2  27332
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-an 362
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