Theorem eumoi 2032

Description: "At most one" inferred from existential uniqueness. (Contributed by NM, 5-Apr-1995.)

Hypothesis

Ref	Expression
eumoi.1	|- E! x ph

Assertion

Ref	Expression
eumoi	|- E* x ph

Proof of Theorem eumoi

Step	Hyp	Ref	Expression
1		eumoi.1	. 2 |- E! x ph
2		eumo 2031	. 2 |- ( E! x ph -> E* x ph )
3	1, 2	ax-mp 5	1 |- E* x ph

Syntax hints:   E!weu 1999   E*wmo 2000

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-mo 2003

This theorem is referenced by:  euxfrdc  2870