Theorem eumoi 2119

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 2118	. 2 ⊢ (∃!𝑥𝜑 → ∃*𝑥𝜑)
3	1, 2	ax-mp 5	1 ⊢ ∃*𝑥𝜑

This proof depends on syntax axioms:  ∃!weu 2086  ∃*wmo 2087

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117  df-mo 2090

This theorem is used by:  euxfrdc  3012