Theorem elfzomin

Description: Membership of an integer in the smallest open range of integers. (Contributed by Alexander van der Vekens, 22-Sep-2018)

	Ref	Expression
Assertion	elfzomin	⊢ ( 𝑍 ∈ ℤ → 𝑍 ∈ ( 𝑍 ..^ ( 𝑍 + 1 ) ) )

Proof

Step	Hyp	Ref	Expression
1		snidg	⊢ ( 𝑍 ∈ ℤ → 𝑍 ∈ { 𝑍 } )
2		fzosn	⊢ ( 𝑍 ∈ ℤ → ( 𝑍 ..^ ( 𝑍 + 1 ) ) = { 𝑍 } )
3	1 2	eleqtrrd	⊢ ( 𝑍 ∈ ℤ → 𝑍 ∈ ( 𝑍 ..^ ( 𝑍 + 1 ) ) )