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Theorem trubifal 1350
Description: A identity. (Contributed by David A. Wheeler, 23-Feb-2018.)
Assertion
Ref Expression
trubifal ((⊤ ↔ ⊥) ↔ ⊥)

Proof of Theorem trubifal
StepHypRef Expression
1 dfbi2 380 . 2 ((⊤ ↔ ⊥) ↔ ((⊤ → ⊥) ∧ (⊥ → ⊤)))
2 truimfal 1344 . . 3 ((⊤ → ⊥) ↔ ⊥)
3 falimtru 1345 . . 3 ((⊥ → ⊤) ↔ ⊤)
42, 3anbi12i 448 . 2 (((⊤ → ⊥) ∧ (⊥ → ⊤)) ↔ (⊥ ∧ ⊤))
5 falantru 1337 . 2 ((⊥ ∧ ⊤) ↔ ⊥)
61, 4, 53bitri 204 1 ((⊤ ↔ ⊥) ↔ ⊥)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  wb 103  wtru 1288  wfal 1292
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-fal 1293
This theorem is referenced by:  falbitru  1351
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