Theorem addscomd

Description: Surreal addition commutes. Part of Theorem 3 of Conway p. 17. (Contributed by Scott Fenton, 20-Aug-2024)

	Ref	Expression
Hypotheses	addscomd.1	|- ( ph -> A e. No )
	addscomd.2	|- ( ph -> B e. No )
Assertion	addscomd	|- ( ph -> ( A +s B ) = ( B +s A ) )

Proof

Step	Hyp	Ref	Expression
1		addscomd.1	|- ( ph -> A e. No )
2		addscomd.2	|- ( ph -> B e. No )
3		addscom	|- ( ( A e. No /\ B e. No ) -> ( A +s B ) = ( B +s A ) )
4	1 2 3	syl2anc	|- ( ph -> ( A +s B ) = ( B +s A ) )