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Theorem trunorfal 1589
Description: A identity. (Contributed by Remi, 25-Oct-2023.) (Proof shortened by Wolf Lammen, 17-Dec-2023.)
Assertion
Ref Expression
trunorfal ((⊤ ⊥) ↔ ⊥)

Proof of Theorem trunorfal
StepHypRef Expression
1 df-nor 1522 . . 3 ((⊤ ⊥) ↔ ¬ (⊤ ∨ ⊥))
2 truorfal 1576 . . 3 ((⊤ ∨ ⊥) ↔ ⊤)
31, 2xchbinx 337 . 2 ((⊤ ⊥) ↔ ¬ ⊤)
4 df-fal 1551 . 2 (⊥ ↔ ¬ ⊤)
53, 4bitr4i 281 1 ((⊤ ⊥) ↔ ⊥)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 209  wo 844   wnor 1521  wtru 1539  wfal 1550
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 210  df-or 845  df-nor 1522  df-tru 1541  df-fal 1551
This theorem is referenced by:  falnortru  1591
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