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Theorem zeo4 16154
Description: An integer is even or odd but not both. With this representation of even and odd integers, this variant of zeo2 12520 follows immediately from the principle of double negation, see notnotb 314. (Contributed by AV, 17-Jun-2021.)
Assertion
Ref Expression
zeo4 (𝑁 ∈ ℤ → (2 ∥ 𝑁 ↔ ¬ ¬ 2 ∥ 𝑁))

Proof of Theorem zeo4
StepHypRef Expression
1 notnotb 314 . 2 (2 ∥ 𝑁 ↔ ¬ ¬ 2 ∥ 𝑁)
21a1i 11 1 (𝑁 ∈ ℤ → (2 ∥ 𝑁 ↔ ¬ ¬ 2 ∥ 𝑁))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 205  wcel 2106   class class class wbr 5103  2c2 12141  cz 12432  cdvds 16070
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
This theorem is referenced by: (None)
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