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Metamath Proof Explorer

Theorem 2ndvdsodd

Description: 2 does not divide an odd number. (Contributed by AV, 18-Jun-2020)

		Ref	Expression
	Assertion	2ndvdsodd	$⊢ Z \in Odd \to \neg 2 ∥ Z$

Step	Hyp	Ref	Expression
1		isodd3	$⊢ Z \in Odd \leftrightarrow (Z \in ℤ \land \neg 2 ∥ Z)$
2	1	simprbi	$⊢ Z \in Odd \to \neg 2 ∥ Z$