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Theorem xorneg 1313
Description: 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 1311 . 2 ((¬ φ ⊻ ¬ ψ) ↔ ¬ (φ ⊻ ¬ ψ))
2 xorneg2 1312 . . 3 ((φ ⊻ ¬ ψ) ↔ ¬ (φψ))
32con2bii 322 . 2 ((φψ) ↔ ¬ (φ ⊻ ¬ ψ))
41, 3bitr4i 243 1 ((¬ φ ⊻ ¬ ψ) ↔ (φψ))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 176  wxo 1304
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 177  df-xor 1305
This theorem is referenced by:  hadnot  1393  had0  1403  mtp-xor  1536
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