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Metamath Proof Explorer

Theorem 19.9h

Description: A wff may be existentially quantified with a variable not free in it. Theorem 19.9 of Margaris p. 89. (Contributed by FL, 24-Mar-2007) (Proof shortened by Wolf Lammen, 5-Jan-2018) (Proof shortened by Wolf Lammen, 14-Jul-2020)

		Ref	Expression
	Hypothesis	19.9h.1	\|- ( ph -> A. x ph )
	Assertion	19.9h	\|- ( E. x ph <-> ph )

Proof

Step	Hyp	Ref	Expression
1		19.9h.1	\|- ( ph -> A. x ph )
2	1	nf5i	\|- F/ x ph
3	2	19.9	\|- ( E. x ph <-> ph )