Theorem eumoi 2500

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 2499	. 2 ⊢ (∃!𝑥𝜑 → ∃*𝑥𝜑)
3	1, 2	ax-mp 5	1 ⊢ ∃*𝑥𝜑

Syntax hints:  ∃!weu 2470  ∃*wmo 2471

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-eu 2474  df-mo 2475

This theorem is referenced by:  euxfr  3392