Theorem cliftetb

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

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

Proof

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