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Metamath Proof Explorer

Theorem nn0ssre

Description: Nonnegative integers are a subset of the reals. (Contributed by Raph Levien, 10-Dec-2002)

		Ref	Expression
	Assertion	nn0ssre	$⊢ ℕ_{0} \subseteq ℝ$

Step	Hyp	Ref	Expression
1		df-n0	$⊢ ℕ_{0} = ℕ \cup \{0\}$
2		nnssre	$⊢ ℕ \subseteq ℝ$
3		0re	$⊢ 0 \in ℝ$
4		snssi	$⊢ 0 \in ℝ \to \{0\} \subseteq ℝ$
5	3 4	ax-mp	$⊢ \{0\} \subseteq ℝ$
6	2 5	unssi	$⊢ ℕ \cup \{0\} \subseteq ℝ$
7	1 6	eqsstri	$⊢ ℕ_{0} \subseteq ℝ$