Theorem naddcomd

Description: Natural addition commutes. Deduction form. (Contributed by Scott Fenton, 30-Jul-2026)

	Ref	Expression
Hypotheses	nadd.1	$$⊢\phi \to A\in \mathrm{On}$$
	nadd.2	$$⊢\phi \to B\in \mathrm{On}$$
Assertion	naddcomd	$$⊢\phi \to A+B=B+A$$

Proof

Step	Hyp	Ref	Expression
1		nadd.1	$$⊢\phi \to A\in \mathrm{On}$$
2		nadd.2	$$⊢\phi \to B\in \mathrm{On}$$
3		naddcom	$$⊢\left(A\in \mathrm{On}\wedge B\in \mathrm{On}\right)\to A+B=B+A$$
4	1 2 3	syl2anc	$$⊢\phi \to A+B=B+A$$