Theorem 19.23

Description: Theorem 19.23 of Margaris p. 90. See 19.23v for a version requiring fewer axioms. (Contributed by NM, 24-Jan-1993) (Revised by Mario Carneiro, 24-Sep-2016)

	Ref	Expression
Hypothesis	19.23.1	|- F/ x ps
Assertion	19.23	|- ( A. x ( ph -> ps ) <-> ( E. x ph -> ps ) )

Proof

Step	Hyp	Ref	Expression
1		19.23.1	|- F/ x ps
2		19.23t	|- ( F/ x ps -> ( A. x ( ph -> ps ) <-> ( E. x ph -> ps ) ) )
3	1 2	ax-mp	|- ( A. x ( ph -> ps ) <-> ( E. x ph -> ps ) )