Theorem negsval2

Description: Surreal negation in terms of subtraction. (Contributed by Scott Fenton, 15-Apr-2025)

	Ref	Expression
Assertion	negsval2	Could not format assertion : No typesetting found for |- ( A e. No -> ( -us ` A ) = ( 0s -s A ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		0sno	Could not format 0s e. No : No typesetting found for |- 0s e. No with typecode |-
2		subsval	Could not format ( ( 0s e. No /\ A e. No ) -> ( 0s -s A ) = ( 0s +s ( -us ` A ) ) ) : No typesetting found for |- ( ( 0s e. No /\ A e. No ) -> ( 0s -s A ) = ( 0s +s ( -us ` A ) ) ) with typecode |-
3	1 2	mpan	Could not format ( A e. No -> ( 0s -s A ) = ( 0s +s ( -us ` A ) ) ) : No typesetting found for |- ( A e. No -> ( 0s -s A ) = ( 0s +s ( -us ` A ) ) ) with typecode |-
4		negscl	Could not format ( A e. No -> ( -us ` A ) e. No ) : No typesetting found for |- ( A e. No -> ( -us ` A ) e. No ) with typecode |-
5		addslid	Could not format ( ( -us ` A ) e. No -> ( 0s +s ( -us ` A ) ) = ( -us ` A ) ) : No typesetting found for |- ( ( -us ` A ) e. No -> ( 0s +s ( -us ` A ) ) = ( -us ` A ) ) with typecode |-
6	4 5	syl	Could not format ( A e. No -> ( 0s +s ( -us ` A ) ) = ( -us ` A ) ) : No typesetting found for |- ( A e. No -> ( 0s +s ( -us ` A ) ) = ( -us ` A ) ) with typecode |-
7	3 6	eqtr2d	Could not format ( A e. No -> ( -us ` A ) = ( 0s -s A ) ) : No typesetting found for |- ( A e. No -> ( -us ` A ) = ( 0s -s A ) ) with typecode |-