Theorem addsassd

Description: Surreal addition is associative. Part of theorem 3 of Conway p. 17. (Contributed by Scott Fenton, 22-Jan-2025)

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

Proof

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