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Theorem bj-trut 34518
Description: A proposition is equivalent to it being implied by T.. Closed form of trud 1408 (which it can shorten); dual of dfnot 1418. It is to tbtru 1409 what a1bi 335 is to tbt 342, and this appears in their respective proofs. (Contributed by BJ, 26-Oct-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-trut  |-  ( ph  <->  ( T.  ->  ph ) )

Proof of Theorem bj-trut
StepHypRef Expression
1 tru 1403 . 2  |- T.
21a1bi 335 1  |-  ( ph  <->  ( T.  ->  ph ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184   T. wtru 1400
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  df-tru 1402
This theorem is referenced by: (None)
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