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Theorem tbt 246
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 245 . . 3  |-  ( (
ph  ->  ps )  <->  ( ph  ->  ( ps  <->  ph ) ) )
32pm5.74ri 180 . 2  |-  ( ph  ->  ( ps  <->  ( ps  <->  ph ) ) )
41, 3ax-mp 5 1  |-  ( ps  <->  ( ps  <->  ph ) )
Colors of variables: wff set class
Syntax hints:    <-> 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:  tbtru  1341  exists1  2093  reu6  2868  eqv  3377  vnex  4054  bj-vprc  13083
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