Theorem exisym1

Description: A symmetry with E. .

See negsym1 for more information. (Contributed by Anthony Hart, 4-Sep-2011)

	Ref	Expression
Assertion	exisym1	$$⊢\exists x\exists x\perp \to \exists x\phi$$

Proof

Step	Hyp	Ref	Expression
1		nfe1	$$⊢Ⅎx\exists x\phi$$
2		falim	$$⊢\perp \to \phi$$
3	2	eximi	$$⊢\exists x\perp \to \exists x\phi$$
4	1 3	exlimi	$$⊢\exists x\exists x\perp \to \exists x\phi$$