Theorem hadifpOLD

Description: Obsolete version of hadifp as of 10-Aug-2026. (Contributed by BJ, 11-Aug-2020) (Proof modification is discouraged.) (New usage is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		had1OLD	|- ( ph -> ( hadd ( ph , ps , ch ) <-> ( ps <-> ch ) ) )
2		had0OLD	|- ( -. ph -> ( hadd ( ph , ps , ch ) <-> ( ps \/_ ch ) ) )
3	1 2	casesifp	|- ( hadd ( ph , ps , ch ) <-> if- ( ph , ( ps <-> ch ) , ( ps \/_ ch ) ) )