Theorem eumoi 2609

Description: Uniqueness 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 2608	. 2 ⊢ (∃!𝑥𝜑 → ∃*𝑥𝜑)
3	1, 2	ax-mp 5	1 ⊢ ∃*𝑥𝜑

This proof depends on syntax axioms:  ∃*wmo 2567  ∃!weu 2598

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-eu 2599

This theorem is used by:  euxfrw  3686  euxfr  3688  axsepgfromrep  5257