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 ( 𝜑 , 𝜓 , 𝜒 ) ↔ if- ( 𝜑 , ( 𝜓 ↔ 𝜒 ) , ( 𝜓 ⊻ 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		had1OLD	⊢ ( 𝜑 → ( hadd ( 𝜑 , 𝜓 , 𝜒 ) ↔ ( 𝜓 ↔ 𝜒 ) ) )
2		had0OLD	⊢ ( ¬ 𝜑 → ( hadd ( 𝜑 , 𝜓 , 𝜒 ) ↔ ( 𝜓 ⊻ 𝜒 ) ) )
3	1 2	casesifp	⊢ ( hadd ( 𝜑 , 𝜓 , 𝜒 ) ↔ if- ( 𝜑 , ( 𝜓 ↔ 𝜒 ) , ( 𝜓 ⊻ 𝜒 ) ) )