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Theorem falantru 1310
Description: A identity. (Contributed by David A. Wheeler, 23-Feb-2018.)
Assertion
Ref Expression
falantru ((⊥ ∧ ⊤) ↔ ⊥)

Proof of Theorem falantru
StepHypRef Expression
1 simpl 106 . 2 ((⊥ ∧ ⊤) → ⊥)
2 falim 1273 . 2 (⊥ → (⊥ ∧ ⊤))
31, 2impbii 121 1 ((⊥ ∧ ⊤) ↔ ⊥)
Colors of variables: wff set class
Syntax hints:  wa 101  wb 102  wtru 1260  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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