Theorem 19.37v

Description: Version of 19.37 with a disjoint variable condition, requiring fewer axioms. (Contributed by NM, 21-Jun-1993)

	Ref	Expression
Assertion	19.37v	|- ( E. x ( ph -> ps ) <-> ( ph -> E. x ps ) )

Proof

Step	Hyp	Ref	Expression
1		19.35	|- ( E. x ( ph -> ps ) <-> ( A. x ph -> E. x ps ) )
2		19.3v	|- ( A. x ph <-> ph )
3	2	imbi1i	|- ( ( A. x ph -> E. x ps ) <-> ( ph -> E. x ps ) )
4	1 3	bitri	|- ( E. x ( ph -> ps ) <-> ( ph -> E. x ps ) )