Theorem moor

Description: "At most one" is still the case when a disjunct is removed. (Contributed by NM, 5-Apr-2004)

	Ref	Expression
Assertion	moor	⊢ ( ∃* 𝑥 ( 𝜑 ∨ 𝜓 ) → ∃* 𝑥 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		orc	⊢ ( 𝜑 → ( 𝜑 ∨ 𝜓 ) )
2	1	moimi	⊢ ( ∃* 𝑥 ( 𝜑 ∨ 𝜓 ) → ∃* 𝑥 𝜑 )