Theorem xorneg

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

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

Proof

Step	Hyp	Ref	Expression
1		xorneg1	⊢ ( ( ¬ 𝜑 ⊻ ¬ 𝜓 ) ↔ ¬ ( 𝜑 ⊻ ¬ 𝜓 ) )
2		xorneg2	⊢ ( ( 𝜑 ⊻ ¬ 𝜓 ) ↔ ¬ ( 𝜑 ⊻ 𝜓 ) )
3	2	con2bii	⊢ ( ( 𝜑 ⊻ 𝜓 ) ↔ ¬ ( 𝜑 ⊻ ¬ 𝜓 ) )
4	1 3	bitr4i	⊢ ( ( ¬ 𝜑 ⊻ ¬ 𝜓 ) ↔ ( 𝜑 ⊻ 𝜓 ) )