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Theorem pm5.1 575
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 pm5.501 243 . 2  |-  ( ph  ->  ( ps  <->  ( ph  <->  ps ) ) )
21biimpa 294 1  |-  ( (
ph  /\  ps )  ->  ( ph  <->  ps )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  pm5.35  887  ssconb  3179
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