Theorem xaddcomd

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

	Ref	Expression
Hypotheses	xaddcomd.1	|- ( ph -> A e. RR* )
	xaddcomd.2	|- ( ph -> B e. RR* )
Assertion	xaddcomd	|- ( ph -> ( A +e B ) = ( B +e A ) )

Proof

Step	Hyp	Ref	Expression
1		xaddcomd.1	|- ( ph -> A e. RR* )
2		xaddcomd.2	|- ( ph -> B e. RR* )
3		xaddcom	|- ( ( A e. RR* /\ B e. RR* ) -> ( A +e B ) = ( B +e A ) )
4	1 2 3	syl2anc	|- ( ph -> ( A +e B ) = ( B +e A ) )