Theorem mulscld

Description: The surreals are closed under multiplication. Theorem 8(i) of Conway p. 19. (Contributed by Scott Fenton, 6-Mar-2025)

	Ref	Expression
Hypotheses	mulscld.1	$$⊢\phi \to A\in \mathrm{No}$$
	mulscld.2	$$⊢\phi \to B\in \mathrm{No}$$
Assertion	mulscld	Could not format assertion : No typesetting found for |- ( ph -> ( A x.s B ) e. No ) with typecode |-

Proof

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