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 ( ph , ps , ch ) <-> hadd ( ph , ch , ps ) )

Proof

Step	Hyp	Ref	Expression
1		wl-3xorcoma	|- ( hadd ( ph , ps , ch ) <-> hadd ( ps , ph , ch ) )
2		wl-3xorrot	|- ( hadd ( ps , ph , ch ) <-> hadd ( ph , ch , ps ) )
3	1 2	bitri	|- ( hadd ( ph , ps , ch ) <-> hadd ( ph , ch , ps ) )