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Metamath Proof Explorer

Theorem nn0xnn0d

Description: A standard nonnegative integer is an extended nonnegative integer, deduction form. (Contributed by AV, 10-Dec-2020)

		Ref	Expression
	Hypothesis	nn0xnn0d.1	$⊢ φ \to A \in ℕ_{0}$
	Assertion	nn0xnn0d	$⊢ φ \to A \in ℕ_{0}^{*}$

Step	Hyp	Ref	Expression
1		nn0xnn0d.1	$⊢ φ \to A \in ℕ_{0}$
2		nn0ssxnn0	$⊢ ℕ_{0} \subseteq ℕ_{0}^{*}$
3	2 1	sselid	$⊢ φ \to A \in ℕ_{0}^{*}$