Theorem eumoi 1933

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

Hypothesis

Ref	Expression
eumoi.1	⊢ ∃!𝑥𝜑

Assertion

Ref	Expression
eumoi	⊢ ∃*𝑥𝜑

Proof of Theorem eumoi

Step	Hyp	Ref	Expression
1		eumoi.1	. 2 ⊢ ∃!𝑥𝜑
2		eumo 1932	. 2 ⊢ (∃!𝑥𝜑 → ∃*𝑥𝜑)
3	1, 2	ax-mp 7	1 ⊢ ∃*𝑥𝜑

Syntax hints:  ∃!weu 1900  ∃*wmo 1901

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-mo 1904

This theorem is referenced by:  euxfrdc  2727