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Theorem trubifal 1323
Description: A identity. (Contributed by David A. Wheeler, 23-Feb-2018.)
Assertion
Ref Expression
trubifal ((⊤ ↔ ⊥) ↔ ⊥)

Proof of Theorem trubifal
StepHypRef Expression
1 dfbi2 374 . 2 ((⊤ ↔ ⊥) ↔ ((⊤ → ⊥) ∧ (⊥ → ⊤)))
2 truimfal 1317 . . 3 ((⊤ → ⊥) ↔ ⊥)
3 falimtru 1318 . . 3 ((⊥ → ⊤) ↔ ⊤)
42, 3anbi12i 441 . 2 (((⊤ → ⊥) ∧ (⊥ → ⊤)) ↔ (⊥ ∧ ⊤))
5 falantru 1310 . 2 ((⊥ ∧ ⊤) ↔ ⊥)
61, 4, 53bitri 199 1 ((⊤ ↔ ⊥) ↔ ⊥)
Colors of variables: wff set class
Syntax hints:  wi 4  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:  falbitru  1324
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