Theorem exmo

Description: Any proposition holds for some x or holds for at most one x . (Contributed by NM, 8-Mar-1995) Shorten proof and avoid df-eu . (Revised by BJ, 14-Oct-2022)

	Ref	Expression
Assertion	exmo	⊢ ( ∃ 𝑥 𝜑 ∨ ∃* 𝑥 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		nexmo	⊢ ( ¬ ∃ 𝑥 𝜑 → ∃* 𝑥 𝜑 )
2	1	orri	⊢ ( ∃ 𝑥 𝜑 ∨ ∃* 𝑥 𝜑 )