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Theorem trubifal 1395
Description: A identity. (Contributed by David A. Wheeler, 23-Feb-2018.)
Assertion
Ref Expression
trubifal ((⊤ ↔ ⊥) ↔ ⊥)

Proof of Theorem trubifal
StepHypRef Expression
1 dfbi2 386 . 2 ((⊤ ↔ ⊥) ↔ ((⊤ → ⊥) ∧ (⊥ → ⊤)))
2 truimfal 1389 . . 3 ((⊤ → ⊥) ↔ ⊥)
3 falimtru 1390 . . 3 ((⊥ → ⊤) ↔ ⊤)
42, 3anbi12i 456 . 2 (((⊤ → ⊥) ∧ (⊥ → ⊤)) ↔ (⊥ ∧ ⊤))
5 falantru 1382 . 2 ((⊥ ∧ ⊤) ↔ ⊥)
61, 4, 53bitri 205 1 ((⊤ ↔ ⊥) ↔ ⊥)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wb 104  wtru 1333  wfal 1337
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605
This theorem depends on definitions:  df-bi 116  df-tru 1335  df-fal 1338
This theorem is referenced by:  falbitru  1396
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