Theorem 19.37

Description: Theorem 19.37 of Margaris p. 90. See 19.37v for a version requiring fewer axioms. (Contributed by NM, 21-Jun-1993)

	Ref	Expression
Hypothesis	19.37.1	|- F/ x ph
Assertion	19.37	|- ( E. x ( ph -> ps ) <-> ( ph -> E. x ps ) )

Proof

Step	Hyp	Ref	Expression
1		19.37.1	|- F/ x ph
2		19.35	|- ( E. x ( ph -> ps ) <-> ( A. x ph -> E. x ps ) )
3	1	19.3	|- ( A. x ph <-> ph )
4	3	imbi1i	|- ( ( A. x ph -> E. x ps ) <-> ( ph -> E. x ps ) )
5	2 4	bitri	|- ( E. x ( ph -> ps ) <-> ( ph -> E. x ps ) )