Theorem eumoi 2579

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 2578	. 2 ⊢ (∃!𝑥𝜑 → ∃*𝑥𝜑)
3	1, 2	ax-mp 5	1 ⊢ ∃*𝑥𝜑

Syntax hints:  ∃*wmo 2538  ∃!weu 2568

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 396  df-eu 2569

This theorem is referenced by:  euxfrw  3651  euxfr  3653  axsepgfromrep  5216