Theorem 0elixp

Description: Membership of the empty set in an infinite Cartesian product. (Contributed by Steve Rodriguez, 29-Sep-2006)

	Ref	Expression
Assertion	0elixp	⊢ ∅ ∈ X 𝑥 ∈ ∅ 𝐴

Proof

Step	Hyp	Ref	Expression
1		0ex	⊢ ∅ ∈ V
2	1	snid	⊢ ∅ ∈ { ∅ }
3		ixp0x	⊢ X 𝑥 ∈ ∅ 𝐴 = { ∅ }
4	2 3	eleqtrri	⊢ ∅ ∈ X 𝑥 ∈ ∅ 𝐴