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Metamath Proof Explorer

Theorem moexexv

Description: "At most one" double quantification. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker moexexvw when possible. (Contributed by NM, 26-Jan-1997) (New usage is discouraged.)

		Ref	Expression
	Assertion	moexexv	⊢ ( ( ∃* 𝑥 𝜑 ∧ ∀ 𝑥 ∃* 𝑦 𝜓 ) → ∃* 𝑦 ∃ 𝑥 ( 𝜑 ∧ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		nfv	⊢ Ⅎ 𝑦 𝜑
2	1	moexex	⊢ ( ( ∃* 𝑥 𝜑 ∧ ∀ 𝑥 ∃* 𝑦 𝜓 ) → ∃* 𝑦 ∃ 𝑥 ( 𝜑 ∧ 𝜓 ) )