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Theorem norcom 1526
Description: The connector is commutative. (Contributed by Remi, 25-Oct-2023.) (Proof shortened by Wolf Lammen, 23-Apr-2024.)
Assertion
Ref Expression
norcom ((𝜑 𝜓) ↔ (𝜓 𝜑))

Proof of Theorem norcom
StepHypRef Expression
1 df-nor 1525 . . 3 ((𝜑 𝜓) ↔ ¬ (𝜑𝜓))
2 orcom 866 . . 3 ((𝜑𝜓) ↔ (𝜓𝜑))
31, 2xchbinx 333 . 2 ((𝜑 𝜓) ↔ ¬ (𝜓𝜑))
4 df-nor 1525 . 2 ((𝜓 𝜑) ↔ ¬ (𝜓𝜑))
53, 4bitr4i 277 1 ((𝜑 𝜓) ↔ (𝜓 𝜑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 205  wo 843   wnor 1524
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 1525
This theorem is referenced by:  norass  1537  norassOLD  1538  falnortru  1594
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