Theorem addscl

Description: Surreal numbers are closed under addition. Theorem 6(iii) of [Conway[ p. 18. (Contributed by Scott Fenton, 21-Jan-2025)

	Ref	Expression
Assertion	addscl	Could not format assertion : No typesetting found for |- ( ( A e. No /\ B e. No ) -> ( A +s B ) e. No ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		simpl	$$⊢\left(A\in \mathrm{No}\wedge B\in \mathrm{No}\right)\to A\in \mathrm{No}$$
2		simpr	$$⊢\left(A\in \mathrm{No}\wedge B\in \mathrm{No}\right)\to B\in \mathrm{No}$$
3	1 2	addscld	Could not format ( ( A e. No /\ B e. No ) -> ( A +s B ) e. No ) : No typesetting found for |- ( ( A e. No /\ B e. No ) -> ( A +s B ) e. No ) with typecode |-