Theorem xorneg

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

	Ref	Expression
Assertion	xorneg	$$⊢\left(\neg \phi ⊻\neg \psi \right)\leftrightarrow \left(\phi ⊻\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		xorneg1	$$⊢\left(\neg \phi ⊻\neg \psi \right)\leftrightarrow \neg \left(\phi ⊻\neg \psi \right)$$
2		xorneg2	$$⊢\left(\phi ⊻\neg \psi \right)\leftrightarrow \neg \left(\phi ⊻\psi \right)$$
3	2	con2bii	$$⊢\left(\phi ⊻\psi \right)\leftrightarrow \neg \left(\phi ⊻\neg \psi \right)$$
4	1 3	bitr4i	$$⊢\left(\neg \phi ⊻\neg \psi \right)\leftrightarrow \left(\phi ⊻\psi \right)$$