Theorem nnnn0d

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

	Ref	Expression
Hypothesis	nnnn0d.1	⊢ ( 𝜑 → 𝐴 ∈ ℕ )
Assertion	nnnn0d	⊢ ( 𝜑 → 𝐴 ∈ ℕ0 )

Proof

Step	Hyp	Ref	Expression
1		nnnn0d.1	⊢ ( 𝜑 → 𝐴 ∈ ℕ )
2		nnssnn0	⊢ ℕ ⊆ ℕ0
3	2 1	sseldi	⊢ ( 𝜑 → 𝐴 ∈ ℕ0 )