Theorem 19.19

Description: Theorem 19.19 of Margaris p. 90. (Contributed by NM, 12-Mar-1993)

	Ref	Expression
Hypothesis	19.19.1	|- F/ x ph
Assertion	19.19	|- ( A. x ( ph <-> ps ) -> ( ph <-> E. x ps ) )

Proof

Step	Hyp	Ref	Expression
1		19.19.1	|- F/ x ph
2	1	19.9	|- ( E. x ph <-> ph )
3		exbi	|- ( A. x ( ph <-> ps ) -> ( E. x ph <-> E. x ps ) )
4	2 3	bitr3id	|- ( A. x ( ph <-> ps ) -> ( ph <-> E. x ps ) )