Theorem exlimimd

Description: Existential elimination rule of natural deduction. (Contributed by ML, 17-Jul-2020)

	Ref	Expression
Hypotheses	exlimimd.1	$$⊢\phi \to \exists x\psi$$
	exlimimd.2	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	exlimimd	$$⊢\phi \to \chi$$

Proof

Step	Hyp	Ref	Expression
1		exlimimd.1	$$⊢\phi \to \exists x\psi$$
2		exlimimd.2	$$⊢\phi \to \left(\psi \to \chi \right)$$
3	2	imp	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
4	1 3	exlimddv	$$⊢\phi \to \chi$$