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Theorem biimt 239
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 5 . 2  |-  ( ps 
->  ( ph  ->  ps ) )
2 pm2.27 39 . 2  |-  ( ph  ->  ( ( ph  ->  ps )  ->  ps )
)
31, 2impbid2 141 1  |-  ( ph  ->  ( ps  <->  ( ph  ->  ps ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  pm5.5  240  a1bi  241  abai  525  dedlem0a  910  ceqsralt  2627  reu8  2789  csbiebt  2943  r19.3rm  3331  fncnv  4990  ovmpt2dxf  5651  brecop  6255
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