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	|- ( E. x ph <-> ph )

Proof

Step	Hyp	Ref	Expression
1		ax5e	|- ( E. x ph -> ph )
2		19.8v	|- ( ph -> E. x ph )
3	1 2	impbii	|- ( E. x ph <-> ph )