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Metamath Proof Explorer

Theorem uzssd

Description: Subset relationship for two sets of upper integers. (Contributed by Glauco Siliprandi, 23-Oct-2021)

		Ref	Expression
	Hypothesis	uzssd.1	$⊢ φ \to N \in ℤ_{\geq M}$
	Assertion	uzssd	$⊢ φ \to ℤ_{\geq N} \subseteq ℤ_{\geq M}$

Step	Hyp	Ref	Expression
1		uzssd.1	$⊢ φ \to N \in ℤ_{\geq M}$
2		uzss	$⊢ N \in ℤ_{\geq M} \to ℤ_{\geq N} \subseteq ℤ_{\geq M}$
3	1 2	syl	$⊢ φ \to ℤ_{\geq N} \subseteq ℤ_{\geq M}$