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Theorem altdftru 25051
Description: Alternate definition of true. In fact any tautology is a definition of true. (Contributed by FL, 23-Mar-2011.)
Assertion
Ref Expression
altdftru  |-  (  T.  <->  (
ph  \/  -.  ph )
)

Proof of Theorem altdftru
StepHypRef Expression
1 df-tru 1310 . 2  |-  (  T.  <->  (
ph 
<-> 
ph ) )
2 exmid 404 . . . 4  |-  ( ph  \/  -.  ph )
32a1i 10 . . 3  |-  ( (
ph 
<-> 
ph )  ->  ( ph  \/  -.  ph )
)
4 biidd 228 . . 3  |-  ( (
ph  \/  -.  ph )  ->  ( ph  <->  ph ) )
53, 4impbii 180 . 2  |-  ( (
ph 
<-> 
ph )  <->  ( ph  \/  -.  ph ) )
61, 5bitri 240 1  |-  (  T.  <->  (
ph  \/  -.  ph )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176    \/ wo 357    T. wtru 1307
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-or 359  df-tru 1310
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