Theorem 2eumo

Description: Nested unique existential quantifier and at-most-one quantifier. (Contributed by NM, 3-Dec-2001)

	Ref	Expression
Assertion	2eumo	⊢ ( ∃! 𝑥 ∃* 𝑦 𝜑 → ∃* 𝑥 ∃! 𝑦 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		euimmo	⊢ ( ∀ 𝑥 ( ∃! 𝑦 𝜑 → ∃* 𝑦 𝜑 ) → ( ∃! 𝑥 ∃* 𝑦 𝜑 → ∃* 𝑥 ∃! 𝑦 𝜑 ) )
2		eumo	⊢ ( ∃! 𝑦 𝜑 → ∃* 𝑦 𝜑 )
3	1 2	mpg	⊢ ( ∃! 𝑥 ∃* 𝑦 𝜑 → ∃* 𝑥 ∃! 𝑦 𝜑 )