Theorem xorneg2

Description: The connector \/_ is negated under negation of one argument. (Contributed by Mario Carneiro, 4-Sep-2016) (Proof shortened by Wolf Lammen, 27-Jun-2020)

	Ref	Expression
Assertion	xorneg2	|- ( ( ph \/_ -. ps ) <-> -. ( ph \/_ ps ) )

Proof

Step	Hyp	Ref	Expression
1		df-xor	|- ( ( ph \/_ -. ps ) <-> -. ( ph <-> -. ps ) )
2		pm5.18	|- ( ( ph <-> ps ) <-> -. ( ph <-> -. ps ) )
3		xnor	|- ( ( ph <-> ps ) <-> -. ( ph \/_ ps ) )
4	1 2 3	3bitr2i	|- ( ( ph \/_ -. ps ) <-> -. ( ph \/_ ps ) )