Theorem hadcomaOLD

Description: Obsolete version of hadcoma as of 17-Dec-2023. (Contributed by Mario Carneiro, 4-Sep-2016) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	hadcomaOLD	|- ( hadd ( ph , ps , ch ) <-> hadd ( ps , ph , ch ) )

Proof

Step	Hyp	Ref	Expression
1		xorcom	|- ( ( ph \/_ ps ) <-> ( ps \/_ ph ) )
2		biid	|- ( ch <-> ch )
3	1 2	xorbi12i	|- ( ( ( ph \/_ ps ) \/_ ch ) <-> ( ( ps \/_ ph ) \/_ ch ) )
4		df-had	|- ( hadd ( ph , ps , ch ) <-> ( ( ph \/_ ps ) \/_ ch ) )
5		df-had	|- ( hadd ( ps , ph , ch ) <-> ( ( ps \/_ ph ) \/_ ch ) )
6	3 4 5	3bitr4i	|- ( hadd ( ph , ps , ch ) <-> hadd ( ps , ph , ch ) )