Theorem wl-3xorcomb

Description: Commutative 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-3xorcomb	⊢ ( hadd ( 𝜑 , 𝜓 , 𝜒 ) ↔ hadd ( 𝜑 , 𝜒 , 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		wl-3xorcoma	⊢ ( hadd ( 𝜑 , 𝜓 , 𝜒 ) ↔ hadd ( 𝜓 , 𝜑 , 𝜒 ) )
2		wl-3xorrot	⊢ ( hadd ( 𝜓 , 𝜑 , 𝜒 ) ↔ hadd ( 𝜑 , 𝜒 , 𝜓 ) )
3	1 2	bitri	⊢ ( hadd ( 𝜑 , 𝜓 , 𝜒 ) ↔ hadd ( 𝜑 , 𝜒 , 𝜓 ) )