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	⊢ ( ( 𝜑 ⊻ ¬ 𝜓 ) ↔ ¬ ( 𝜑 ⊻ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		df-xor	⊢ ( ( 𝜑 ⊻ ¬ 𝜓 ) ↔ ¬ ( 𝜑 ↔ ¬ 𝜓 ) )
2		pm5.18	⊢ ( ( 𝜑 ↔ 𝜓 ) ↔ ¬ ( 𝜑 ↔ ¬ 𝜓 ) )
3		xnor	⊢ ( ( 𝜑 ↔ 𝜓 ) ↔ ¬ ( 𝜑 ⊻ 𝜓 ) )
4	1 2 3	3bitr2i	⊢ ( ( 𝜑 ⊻ ¬ 𝜓 ) ↔ ¬ ( 𝜑 ⊻ 𝜓 ) )