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Theorem falantru 1403
Description: A identity. (Contributed by David A. Wheeler, 23-Feb-2018.)
Assertion
Ref Expression
falantru ((⊥ ∧ ⊤) ↔ ⊥)

Proof of Theorem falantru
StepHypRef Expression
1 simpl 109 . 2 ((⊥ ∧ ⊤) → ⊥)
2 falim 1367 . 2 (⊥ → (⊥ ∧ ⊤))
31, 2impbii 126 1 ((⊥ ∧ ⊤) ↔ ⊥)
Colors of variables: wff set class
Syntax hints:  wa 104  wb 105  wtru 1354  wfal 1358
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-fal 1359
This theorem is referenced by:  trubifal  1416  falxortru  1421  falxorfal  1422
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