Theorem nn0xnn0d

Description: A standard nonnegative integer is an extended nonnegative integer, deduction form. (Contributed by AV, 10-Dec-2020)

	Ref	Expression
Hypothesis	nn0xnn0d.1	⊢ ( 𝜑 → 𝐴 ∈ ℕ0 )
Assertion	nn0xnn0d	⊢ ( 𝜑 → 𝐴 ∈ ℕ0* )

Proof

Step	Hyp	Ref	Expression
1		nn0xnn0d.1	⊢ ( 𝜑 → 𝐴 ∈ ℕ0 )
2		nn0ssxnn0	⊢ ℕ0 ⊆ ℕ0*
3	2 1	sseldi	⊢ ( 𝜑 → 𝐴 ∈ ℕ0* )