Theorem mormo

Description: Unrestricted "at most one" implies restricted "at most one". (Contributed by NM, 16-Jun-2017)

	Ref	Expression
Assertion	mormo	⊢ ( ∃* 𝑥 𝜑 → ∃* 𝑥 ∈ 𝐴 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		moan	⊢ ( ∃* 𝑥 𝜑 → ∃* 𝑥 ( 𝑥 ∈ 𝐴 ∧ 𝜑 ) )
2		df-rmo	⊢ ( ∃* 𝑥 ∈ 𝐴 𝜑 ↔ ∃* 𝑥 ( 𝑥 ∈ 𝐴 ∧ 𝜑 ) )
3	1 2	sylibr	⊢ ( ∃* 𝑥 𝜑 → ∃* 𝑥 ∈ 𝐴 𝜑 )