Theorem divscl

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

	Ref	Expression
Assertion	divscl	Could not format assertion : No typesetting found for |- ( ( A e. No /\ B e. No /\ B =/= 0s ) -> ( A /su B ) e. No ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		recsex	Could not format ( ( B e. No /\ B =/= 0s ) -> E. x e. No ( B x.s x ) = 1s ) : No typesetting found for |- ( ( B e. No /\ B =/= 0s ) -> E. x e. No ( B x.s x ) = 1s ) with typecode |-
2	1	3adant1	Could not format ( ( A e. No /\ B e. No /\ B =/= 0s ) -> E. x e. No ( B x.s x ) = 1s ) : No typesetting found for |- ( ( A e. No /\ B e. No /\ B =/= 0s ) -> E. x e. No ( B x.s x ) = 1s ) with typecode |-
3		divsclw	Could not format ( ( ( A e. No /\ B e. No /\ B =/= 0s ) /\ E. x e. No ( B x.s x ) = 1s ) -> ( A /su B ) e. No ) : No typesetting found for |- ( ( ( A e. No /\ B e. No /\ B =/= 0s ) /\ E. x e. No ( B x.s x ) = 1s ) -> ( A /su B ) e. No ) with typecode |-
4	2 3	mpdan	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 |-