Theorem exlimimddOLD

Description: Obsolete version of exlimimdd as of 3-Sep-2023. (Contributed by ML, 17-Jul-2020) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	exlimdd.1	$$⊢Ⅎx\phi$$
	exlimdd.2	$$⊢Ⅎx\chi$$
	exlimdd.3	$$⊢\phi \to \exists x\psi$$
	exlimimddOLD.4	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	exlimimddOLD	$$⊢\phi \to \chi$$

Proof

Step	Hyp	Ref	Expression
1		exlimdd.1	$$⊢Ⅎx\phi$$
2		exlimdd.2	$$⊢Ⅎx\chi$$
3		exlimdd.3	$$⊢\phi \to \exists x\psi$$
4		exlimimddOLD.4	$$⊢\phi \to \left(\psi \to \chi \right)$$
5	4	imp	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
6	1 2 3 5	exlimdd	$$⊢\phi \to \chi$$