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Theorem nbi2 935
Description: Two ways to express "exclusive or." (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 24-Jan-2013.)
Assertion
Ref Expression
nbi2 (¬ (𝜑𝜓) ↔ ((𝜑𝜓) ∧ ¬ (𝜑𝜓)))

Proof of Theorem nbi2
StepHypRef Expression
1 xor3 372 . 2 (¬ (𝜑𝜓) ↔ (𝜑 ↔ ¬ 𝜓))
2 pm5.17 931 . 2 (((𝜑𝜓) ∧ ¬ (𝜑𝜓)) ↔ (𝜑 ↔ ¬ 𝜓))
31, 2bitr4i 267 1 (¬ (𝜑𝜓) ↔ ((𝜑𝜓) ∧ ¬ (𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196  wo 383  wa 384
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 197  df-or 385  df-an 386
This theorem is referenced by:  xor2  1467
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