Theorem naddlidd

Description: Identity law for natural addition. Deduction form. (Contributed by Scott Fenton, 30-Jul-2026)

	Ref	Expression
Hypothesis	nadd.1	$$⊢\phi \to A\in \mathrm{On}$$
Assertion	naddlidd	$$⊢\phi \to \varnothing +A=A$$

Proof

Step	Hyp	Ref	Expression
1		nadd.1	$$⊢\phi \to A\in \mathrm{On}$$
2		naddlid	$$⊢A\in \mathrm{On}\to \varnothing +A=A$$
3	1 2	syl	$$⊢\phi \to \varnothing +A=A$$