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	$$⊢hadd\left(\phi ,\psi ,\chi \right)\leftrightarrow if-\left(\phi ,\left(\psi \leftrightarrow \chi \right),\left(\psi ⊻\chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		had1OLD	$$⊢\phi \to \left(hadd\left(\phi ,\psi ,\chi \right)\leftrightarrow \left(\psi \leftrightarrow \chi \right)\right)$$
2		had0OLD	$$⊢\neg \phi \to \left(hadd\left(\phi ,\psi ,\chi \right)\leftrightarrow \left(\psi ⊻\chi \right)\right)$$
3	1 2	casesifp	$$⊢hadd\left(\phi ,\psi ,\chi \right)\leftrightarrow if-\left(\phi ,\left(\psi \leftrightarrow \chi \right),\left(\psi ⊻\chi \right)\right)$$