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Theorem biimt 240
Description: A wff is equivalent to itself with true antecedent. (Contributed by NM, 28-Jan-1996.)
Assertion
Ref Expression
biimt  |-  ( ph  ->  ( ps  <->  ( ph  ->  ps ) ) )

Proof of Theorem biimt
StepHypRef Expression
1 ax-1 6 . 2  |-  ( ps 
->  ( ph  ->  ps ) )
2 pm2.27 40 . 2  |-  ( ph  ->  ( ( ph  ->  ps )  ->  ps )
)
31, 2impbid2 142 1  |-  ( ph  ->  ( ps  <->  ( ph  ->  ps ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> 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:  pm5.5  241  a1bi  242  abai  532  dedlem0a  935  ceqsralt  2685  reu8  2851  csbiebt  3007  r19.3rm  3419  fncnv  5157  ovmpodxf  5862  brecop  6485  tgss2  12154
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