Theorem wl-3xornot1

Description: Flipping the first input flips the triple xor. wl-3xorrot can rotate any input to the front, so flipping any one of them does the same. (Contributed by Wolf Lammen, 1-May-2024)

	Ref	Expression
Assertion	wl-3xornot1	|- ( -. hadd ( ph , ps , ch ) <-> hadd ( -. ph , ps , ch ) )

Proof

Step	Hyp	Ref	Expression
1		wl-3xorbi	|- ( hadd ( -. ph , ps , ch ) <-> ( -. ph <-> ( ps <-> ch ) ) )
2		nbbn	|- ( ( -. ph <-> ( ps <-> ch ) ) <-> -. ( ph <-> ( ps <-> ch ) ) )
3		wl-3xorbi	|- ( hadd ( ph , ps , ch ) <-> ( ph <-> ( ps <-> ch ) ) )
4	2 3	xchbinxr	|- ( ( -. ph <-> ( ps <-> ch ) ) <-> -. hadd ( ph , ps , ch ) )
5	1 4	bitr2i	|- ( -. hadd ( ph , ps , ch ) <-> hadd ( -. ph , ps , ch ) )