Theorem nnne0d

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

	Ref	Expression
Hypothesis	nnge1d.1	⊢ ( 𝜑 → 𝐴 ∈ ℕ )
Assertion	nnne0d	⊢ ( 𝜑 → 𝐴 ≠ 0 )

Proof

Step	Hyp	Ref	Expression
1		nnge1d.1	⊢ ( 𝜑 → 𝐴 ∈ ℕ )
2		nnne0	⊢ ( 𝐴 ∈ ℕ → 𝐴 ≠ 0 )
3	1 2	syl	⊢ ( 𝜑 → 𝐴 ≠ 0 )