Theorem xaddcomd

Description: The extended real addition operation is commutative. (Contributed by Glauco Siliprandi, 17-Aug-2020)

	Ref	Expression
Hypotheses	xaddcomd.1	$$⊢\phi \to A\in {ℝ}^{*}$$
	xaddcomd.2	$$⊢\phi \to B\in {ℝ}^{*}$$
Assertion	xaddcomd	$$⊢\phi \to A{+}_{𝑒}B=B{+}_{𝑒}A$$

Proof

Step	Hyp	Ref	Expression
1		xaddcomd.1	$$⊢\phi \to A\in {ℝ}^{*}$$
2		xaddcomd.2	$$⊢\phi \to B\in {ℝ}^{*}$$
3		xaddcom	$$⊢\left(A\in {ℝ}^{*}\wedge B\in {ℝ}^{*}\right)\to A{+}_{𝑒}B=B{+}_{𝑒}A$$
4	1 2 3	syl2anc	$$⊢\phi \to A{+}_{𝑒}B=B{+}_{𝑒}A$$