Theorem mulsassd

Description: Associative law for surreal multiplication. Part of theorem 7 of Conway p. 19. (Contributed by Scott Fenton, 10-Mar-2025)

	Ref	Expression
Hypotheses	mulsassd.1	$$⊢\phi \to A\in \mathrm{No}$$
	mulsassd.2	$$⊢\phi \to B\in \mathrm{No}$$
	mulsassd.3	$$⊢\phi \to C\in \mathrm{No}$$
Assertion	mulsassd	Could not format assertion : No typesetting found for |- ( ph -> ( ( A x.s B ) x.s C ) = ( A x.s ( B x.s C ) ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		mulsassd.1	$$⊢\phi \to A\in \mathrm{No}$$
2		mulsassd.2	$$⊢\phi \to B\in \mathrm{No}$$
3		mulsassd.3	$$⊢\phi \to C\in \mathrm{No}$$
4		mulsass	Could not format ( ( A e. No /\ B e. No /\ C e. No ) -> ( ( A x.s B ) x.s C ) = ( A x.s ( B x.s C ) ) ) : No typesetting found for |- ( ( A e. No /\ B e. No /\ C e. No ) -> ( ( A x.s B ) x.s C ) = ( A x.s ( B x.s C ) ) ) with typecode |-
5	1 2 3 4	syl3anc	Could not format ( ph -> ( ( A x.s B ) x.s C ) = ( A x.s ( B x.s C ) ) ) : No typesetting found for |- ( ph -> ( ( A x.s B ) x.s C ) = ( A x.s ( B x.s C ) ) ) with typecode |-