Theorem mulscomd

Description: Surreal multiplication commutes. Part of theorem 7 of Conway p. 19. (Contributed by Scott Fenton, 6-Mar-2025)

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

Proof

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