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Theorem tbt 342
Description: A wff is equivalent to its equivalence with a truth. (Contributed by NM, 18-Aug-1993.) (Proof shortened by Andrew Salmon, 13-May-2011.)
Hypothesis
Ref Expression
tbt.1  |-  ph
Assertion
Ref Expression
tbt  |-  ( ps  <->  ( ps  <->  ph ) )

Proof of Theorem tbt
StepHypRef Expression
1 tbt.1 . 2  |-  ph
2 ibibr 341 . . 3  |-  ( (
ph  ->  ps )  <->  ( ph  ->  ( ps  <->  ph ) ) )
32pm5.74ri 246 . 2  |-  ( ph  ->  ( ps  <->  ( ps  <->  ph ) ) )
41, 3ax-mp 5 1  |-  ( ps  <->  ( ps  <->  ph ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185
This theorem is referenced by:  tbtru  1415  falbitru  1444  exists1  2339  reu6  3237  eqv  3754  vprc  4531  elnev  36173
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