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Metamath Proof Explorer

Theorem eumoi

Description: Uniqueness inferred from existential uniqueness. (Contributed by NM, 5-Apr-1995)

Ref Expression
Hypothesis eumoi.1 ⊢ ∃! 𝑥 𝜑
Assertion eumoi ∃* 𝑥 𝜑

Proof

Step Hyp Ref Expression
1 eumoi.1 ⊢ ∃! 𝑥 𝜑
2 eumo ⊢ ( ∃! 𝑥 𝜑 → ∃* 𝑥 𝜑 )
3 1 2 ax-mp ⊢ ∃* 𝑥 𝜑