Theorem 19.9v

Description: Version of 19.9 with a disjoint variable condition, requiring fewer axioms. Any formula can be existentially quantified using a variable which it does not contain. See also 19.3v . (Contributed by NM, 28-May-1995) Remove dependency on ax-7 . (Revised by Wolf Lammen, 4-Dec-2017)

	Ref	Expression
Assertion	19.9v	$$⊢\exists x\phi \leftrightarrow \phi$$

Proof

Step	Hyp	Ref	Expression
1		ax5e	$$⊢\exists x\phi \to \phi$$
2		19.8v	$$⊢\phi \to \exists x\phi$$
3	1 2	impbii	$$⊢\exists x\phi \leftrightarrow \phi$$