Theorem wl-3xorrot

Description: Rotation law for triple xor. (Contributed by Mario Carneiro, 4-Sep-2016) df-had redefined. (Revised by Wolf Lammen, 24-Apr-2024)

	Ref	Expression
Assertion	wl-3xorrot	⊢ ( hadd ( 𝜑 , 𝜓 , 𝜒 ) ↔ hadd ( 𝜓 , 𝜒 , 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		bicom	⊢ ( ( 𝜑 ↔ ( 𝜓 ↔ 𝜒 ) ) ↔ ( ( 𝜓 ↔ 𝜒 ) ↔ 𝜑 ) )
2		wl-3xorbi	⊢ ( hadd ( 𝜑 , 𝜓 , 𝜒 ) ↔ ( 𝜑 ↔ ( 𝜓 ↔ 𝜒 ) ) )
3		wl-3xorbi2	⊢ ( hadd ( 𝜓 , 𝜒 , 𝜑 ) ↔ ( ( 𝜓 ↔ 𝜒 ) ↔ 𝜑 ) )
4	1 2 3	3bitr4i	⊢ ( hadd ( 𝜑 , 𝜓 , 𝜒 ) ↔ hadd ( 𝜓 , 𝜒 , 𝜑 ) )