Theorem nnne0d

Description: A positive integer is nonzero. (Contributed by Mario Carneiro, 27-May-2016)

	Ref	Expression
Hypothesis	nnge1d.1	$$⊢\phi \to A\in \mathbb{N}$$
Assertion	nnne0d	$$⊢\phi \to A\ne 0$$

Proof

Step	Hyp	Ref	Expression
1		nnge1d.1	$$⊢\phi \to A\in \mathbb{N}$$
2		nnne0	$$⊢A\in \mathbb{N}\to A\ne 0$$
3	1 2	syl	$$⊢\phi \to A\ne 0$$