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Metamath Proof Explorer

Theorem uznnssnn

Description: The upper integers starting from a natural are a subset of the naturals. (Contributed by Scott Fenton, 29-Jun-2013)

		Ref	Expression
	Assertion	uznnssnn	$⊢ N \in ℕ \to ℤ_{\geq N} \subseteq ℕ$

Step	Hyp	Ref	Expression
1		elnnuz	$⊢ N \in ℕ \leftrightarrow N \in ℤ_{\geq 1}$
2		uzss	$⊢ N \in ℤ_{\geq 1} \to ℤ_{\geq N} \subseteq ℤ_{\geq 1}$
3	1 2	sylbi	$⊢ N \in ℕ \to ℤ_{\geq N} \subseteq ℤ_{\geq 1}$
4		nnuz	$⊢ ℕ = ℤ_{\geq 1}$
5	3 4	sseqtrrdi	$⊢ N \in ℕ \to ℤ_{\geq N} \subseteq ℕ$