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Theorem xorneg 1519
Description: The connector is unchanged under negation of both arguments. (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
xorneg ((¬ 𝜑 ⊻ ¬ 𝜓) ↔ (𝜑𝜓))

Proof of Theorem xorneg
StepHypRef Expression
1 xorneg1 1518 . 2 ((¬ 𝜑 ⊻ ¬ 𝜓) ↔ ¬ (𝜑 ⊻ ¬ 𝜓))
2 xorneg2 1517 . . 3 ((𝜑 ⊻ ¬ 𝜓) ↔ ¬ (𝜑𝜓))
32con2bii 358 . 2 ((𝜑𝜓) ↔ ¬ (𝜑 ⊻ ¬ 𝜓))
41, 3bitr4i 277 1 ((¬ 𝜑 ⊻ ¬ 𝜓) ↔ (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 205  wxo 1506
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-xor 1507
This theorem is referenced by: (None)
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