Theorem exlimddv

Description: Existential elimination rule of natural deduction (Rule C, explained in exlimiv ). (Contributed by Mario Carneiro, 15-Jun-2016)

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

Proof

Step	Hyp	Ref	Expression
1		exlimddv.1	$$⊢\phi \to \exists x\psi$$
2		exlimddv.2	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
3	2	ex	$$⊢\phi \to \left(\psi \to \chi \right)$$
4	3	exlimdv	$$⊢\phi \to \left(\exists x\psi \to \chi \right)$$
5	1 4	mpd	$$⊢\phi \to \chi$$