This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem euex

Description: Existential uniqueness implies existence. (Contributed by NM, 15-Sep-1993) (Proof shortened by Andrew Salmon, 9-Jul-2011) (Proof shortened by Wolf Lammen, 4-Dec-2018) (Proof shortened by BJ, 7-Oct-2022)

		Ref	Expression
	Assertion	euex	\|- ( E! x ph -> E. x ph )

Proof

Step	Hyp	Ref	Expression
1		df-eu	\|- ( E! x ph <-> ( E. x ph /\ E* x ph ) )
2	1	simplbi	\|- ( E! x ph -> E. x ph )