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Theorem falantru 1310
Description: A  /\ identity. (Contributed by David A. Wheeler, 23-Feb-2018.)
Assertion
Ref Expression
falantru  |-  ( ( F.  /\ T.  )  <-> F.  )

Proof of Theorem falantru
StepHypRef Expression
1 simpl 106 . 2  |-  ( ( F.  /\ T.  )  -> F.  )
2 falim 1273 . 2  |-  ( F. 
->  ( F.  /\ T.  ) )
31, 2impbii 121 1  |-  ( ( F.  /\ T.  )  <-> F.  )
Colors of variables: wff set class
Syntax hints:    /\ wa 101    <-> wb 102   T. wtru 1260   F. wfal 1264
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-fal 1265
This theorem is referenced by:  trubifal  1323  falxortru  1328  falxorfal  1329
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