Theorem wl-df3xor3

Description: Alternative form of wl-df3xor2 . Copy of df-had . (Contributed by Mario Carneiro, 4-Sep-2016) df-had redefined. (Revised by Wolf Lammen, 1-May-2024)

	Ref	Expression
Assertion	wl-df3xor3	|- ( hadd ( ph , ps , ch ) <-> ( ( ph \/_ ps ) \/_ ch ) )

Proof

Step	Hyp	Ref	Expression
1		wl-df3xor2	|- ( hadd ( ph , ps , ch ) <-> ( ph \/_ ( ps \/_ ch ) ) )
2		xorass	|- ( ( ( ph \/_ ps ) \/_ ch ) <-> ( ph \/_ ( ps \/_ ch ) ) )
3	1 2	bitr4i	|- ( hadd ( ph , ps , ch ) <-> ( ( ph \/_ ps ) \/_ ch ) )