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Theorem tbt 245
Description: A wff is equivalent to its equivalence with 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 244 . . 3  |-  ( (
ph  ->  ps )  <->  ( ph  ->  ( ps  <->  ph ) ) )
32pm5.74ri 179 . 2  |-  ( ph  ->  ( ps  <->  ( ps  <->  ph ) ) )
41, 3ax-mp 7 1  |-  ( ps  <->  ( ps  <->  ph ) )
Colors of variables: wff set class
Syntax hints:    <-> 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:  tbtru  1295  exists1  2039  reu6  2790  eqv  3283  vprc  3929  bj-vprc  10972
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