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Metamath Proof Explorer

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 ) )