Theorem subscl

Description: Closure law for surreal subtraction. (Contributed by Scott Fenton, 3-Feb-2025)

	Ref	Expression
Assertion	subscl	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		subsval	Could not format ( ( A e. No /\ B e. No ) -> ( A -s B ) = ( A +s ( -us ` B ) ) ) : No typesetting found for |- ( ( A e. No /\ B e. No ) -> ( A -s B ) = ( A +s ( -us ` B ) ) ) with typecode |-
2		negscl	Could not format ( B e. No -> ( -us ` B ) e. No ) : No typesetting found for |- ( B e. No -> ( -us ` B ) e. No ) with typecode |-
3		addscl	Could not format ( ( A e. No /\ ( -us ` B ) e. No ) -> ( A +s ( -us ` B ) ) e. No ) : No typesetting found for |- ( ( A e. No /\ ( -us ` B ) e. No ) -> ( A +s ( -us ` B ) ) e. No ) with typecode |-
4	2 3	sylan2	Could not format ( ( A e. No /\ B e. No ) -> ( A +s ( -us ` B ) ) e. No ) : No typesetting found for |- ( ( A e. No /\ B e. No ) -> ( A +s ( -us ` B ) ) e. No ) with typecode |-
5	1 4	eqeltrd	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 |-