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Theorem xorneg 1473
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 1472 . 2 ((¬ 𝜑 ⊻ ¬ 𝜓) ↔ ¬ (𝜑 ⊻ ¬ 𝜓))
2 xorneg2 1471 . . 3 ((𝜑 ⊻ ¬ 𝜓) ↔ ¬ (𝜑𝜓))
32con2bii 347 . 2 ((𝜑𝜓) ↔ ¬ (𝜑 ⊻ ¬ 𝜓))
41, 3bitr4i 267 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: (None)
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