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Metamath Proof Explorer

Theorem bnj923

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

		Ref	Expression
	Hypothesis	bnj923.1	$⊢ D = ω ∖ \{\emptyset\}$
	Assertion	bnj923	$⊢ n \in D \to n \in ω$

Step	Hyp	Ref	Expression
1		bnj923.1	$⊢ D = ω ∖ \{\emptyset\}$
2		eldifi	$⊢ n \in (ω ∖ \{\emptyset\}) \to n \in ω$
3	2 1	eleq2s	$⊢ n \in D \to n \in ω$