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

Proof

Step	Hyp	Ref	Expression
1		bicom	|- ( ( ph <-> ( ps <-> ch ) ) <-> ( ( ps <-> ch ) <-> ph ) )
2		wl-3xorbi	|- ( hadd ( ph , ps , ch ) <-> ( ph <-> ( ps <-> ch ) ) )
3		wl-3xorbi2	|- ( hadd ( ps , ch , ph ) <-> ( ( ps <-> ch ) <-> ph ) )
4	1 2 3	3bitr4i	|- ( hadd ( ph , ps , ch ) <-> hadd ( ps , ch , ph ) )