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Metamath Proof Explorer

Theorem evenelz

Description: An even number is an integer. This follows immediately from the reverse closure of the divides relation, see dvdszrcl . (Contributed by AV, 22-Jun-2021)

		Ref	Expression
	Assertion	evenelz	$⊢ 2 ∥ N \to N \in ℤ$

Proof

Step	Hyp	Ref	Expression
1		dvdszrcl	$⊢ 2 ∥ N \to (2 \in ℤ \land N \in ℤ)$
2	1	simprd	$⊢ 2 ∥ N \to N \in ℤ$