Theorem clifteta

Description: show d is the same as an if-else involving a,b. (Contributed by Jarvin Udandy, 20-Sep-2020)

	Ref	Expression
Hypotheses	clifteta.1	$$⊢\left(\left(\phi \wedge \neg \chi \right)\vee \left(\psi \wedge \chi \right)\right)$$
	clifteta.2	$$⊢\theta$$
Assertion	clifteta	$$⊢\theta \leftrightarrow \left(\left(\phi \wedge \neg \chi \right)\vee \left(\psi \wedge \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		clifteta.1	$$⊢\left(\left(\phi \wedge \neg \chi \right)\vee \left(\psi \wedge \chi \right)\right)$$
2		clifteta.2	$$⊢\theta$$
3	2 1	2th	$$⊢\theta \leftrightarrow \left(\left(\phi \wedge \neg \chi \right)\vee \left(\psi \wedge \chi \right)\right)$$