Theorem divscld

Description: Surreal division closure law. (Contributed by Scott Fenton, 16-Mar-2025)

	Ref	Expression
Hypotheses	divscld.1	$$⊢\phi \to A\in \mathrm{No}$$
	divscld.2	$$⊢\phi \to B\in \mathrm{No}$$
	divscld.3	No typesetting found for |- ( ph -> B =/= 0s ) with typecode |-
Assertion	divscld	Could not format assertion : No typesetting found for |- ( ph -> ( A /su B ) e. No ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		divscld.1	$$⊢\phi \to A\in \mathrm{No}$$
2		divscld.2	$$⊢\phi \to B\in \mathrm{No}$$
3		divscld.3	Could not format ( ph -> B =/= 0s ) : No typesetting found for |- ( ph -> B =/= 0s ) with typecode |-
4		divscl	Could not format ( ( A e. No /\ B e. No /\ B =/= 0s ) -> ( A /su B ) e. No ) : No typesetting found for |- ( ( A e. No /\ B e. No /\ B =/= 0s ) -> ( A /su B ) e. No ) with typecode |-
5	1 2 3 4	syl3anc	Could not format ( ph -> ( A /su B ) e. No ) : No typesetting found for |- ( ph -> ( A /su B ) e. No ) with typecode |-