Theorem nna0

Description: Addition with zero. Theorem 4I(A1) of Enderton p. 79. (Contributed by NM, 20-Sep-1995)

	Ref	Expression
Assertion	nna0	$$⊢A\in \mathrm{\omega }\to A{+}_{𝑜}\varnothing =A$$

Proof

Step	Hyp	Ref	Expression
1		nnon	$$⊢A\in \mathrm{\omega }\to A\in \mathrm{On}$$
2		oa0	$$⊢A\in \mathrm{On}\to A{+}_{𝑜}\varnothing =A$$
3	1 2	syl	$$⊢A\in \mathrm{\omega }\to A{+}_{𝑜}\varnothing =A$$