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	$$⊢\phi \to A\in \mathrm{No}$$
	addscomd.2	$$⊢\phi \to B\in \mathrm{No}$$
Assertion	addscomd	Could not format assertion : No typesetting found for |- ( ph -> ( A +s B ) = ( B +s A ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		addscomd.1	$$⊢\phi \to A\in \mathrm{No}$$
2		addscomd.2	$$⊢\phi \to B\in \mathrm{No}$$
3		addscom	Could not format ( ( A e. No /\ B e. No ) -> ( A +s B ) = ( B +s A ) ) : No typesetting found for |- ( ( A e. No /\ B e. No ) -> ( A +s B ) = ( B +s A ) ) with typecode |-
4	1 2 3	syl2anc	Could not format ( ph -> ( A +s B ) = ( B +s A ) ) : No typesetting found for |- ( ph -> ( A +s B ) = ( B +s A ) ) with typecode |-