Theorem xorneg 1515

Description: The connector ⊻ is unchanged under negation of both arguments. (Contributed by Mario Carneiro, 4-Sep-2016.)

Assertion

Ref	Expression
xorneg	⊢ ((¬ 𝜑 ⊻ ¬ 𝜓) ↔ (𝜑 ⊻ 𝜓))

Proof of Theorem xorneg

Step	Hyp	Ref	Expression
1		xorneg1 1514	. 2 ⊢ ((¬ 𝜑 ⊻ ¬ 𝜓) ↔ ¬ (𝜑 ⊻ ¬ 𝜓))
2		xorneg2 1513	. . 3 ⊢ ((𝜑 ⊻ ¬ 𝜓) ↔ ¬ (𝜑 ⊻ 𝜓))
3	2	con2bii 361	. 2 ⊢ ((𝜑 ⊻ 𝜓) ↔ ¬ (𝜑 ⊻ ¬ 𝜓))
4	1, 3	bitr4i 281	1 ⊢ ((¬ 𝜑 ⊻ ¬ 𝜓) ↔ (𝜑 ⊻ 𝜓))

Syntax hints:  ¬ wn 3   ↔ wb 209   ⊻ wxo 1502

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 210  df-xor 1503

This theorem is referenced by: (None)