Theorem nn0sscn

Description: Nonnegative integers are a subset of the complex numbers. (Contributed by NM, 9-May-2004) Reduce dependencies on axioms. (Revised by Steven Nguyen, 8-Oct-2022)

	Ref	Expression
Assertion	nn0sscn	⊢ ℕ0 ⊆ ℂ

Proof

Step	Hyp	Ref	Expression
1		df-n0	⊢ ℕ0 = ( ℕ ∪ { 0 } )
2		nnsscn	⊢ ℕ ⊆ ℂ
3		0cn	⊢ 0 ∈ ℂ
4		snssi	⊢ ( 0 ∈ ℂ → { 0 } ⊆ ℂ )
5	3 4	ax-mp	⊢ { 0 } ⊆ ℂ
6	2 5	unssi	⊢ ( ℕ ∪ { 0 } ) ⊆ ℂ
7	1 6	eqsstri	⊢ ℕ0 ⊆ ℂ