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Theorem xorneg2 1471
Description: The connector is negated under negation of one argument. (Contributed by Mario Carneiro, 4-Sep-2016.) (Proof shortened by Wolf Lammen, 27-Jun-2020.)
Assertion
Ref Expression
xorneg2 ((𝜑 ⊻ ¬ 𝜓) ↔ ¬ (𝜑𝜓))

Proof of Theorem xorneg2
StepHypRef Expression
1 df-xor 1462 . 2 ((𝜑 ⊻ ¬ 𝜓) ↔ ¬ (𝜑 ↔ ¬ 𝜓))
2 pm5.18 371 . 2 ((𝜑𝜓) ↔ ¬ (𝜑 ↔ ¬ 𝜓))
3 xnor 1463 . 2 ((𝜑𝜓) ↔ ¬ (𝜑𝜓))
41, 2, 33bitr2i 288 1 ((𝜑 ⊻ ¬ 𝜓) ↔ ¬ (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196  wxo 1461
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-xor 1462
This theorem is referenced by:  xorneg1  1472  xorneg  1473
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