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Theorem trunortru 1588
Description: A identity. (Contributed by Remi, 25-Oct-2023.) (Proof shortened by Wolf Lammen, 7-Dec-2023.)
Assertion
Ref Expression
trunortru ((⊤ ⊤) ↔ ⊥)

Proof of Theorem trunortru
StepHypRef Expression
1 df-nor 1523 . . 3 ((⊤ ⊤) ↔ ¬ (⊤ ∨ ⊤))
2 truortru 1576 . . 3 ((⊤ ∨ ⊤) ↔ ⊤)
31, 2xchbinx 333 . 2 ((⊤ ⊤) ↔ ¬ ⊤)
4 df-fal 1552 . 2 (⊥ ↔ ¬ ⊤)
53, 4bitr4i 277 1 ((⊤ ⊤) ↔ ⊥)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 205  wo 843   wnor 1522  wtru 1540  wfal 1551
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 206  df-or 844  df-nor 1523  df-fal 1552
This theorem is referenced by: (None)
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