Theorem negsidd

Description: Surreal addition of a number and its negative. Theorem 4(iii) of Conway p. 17. (Contributed by Scott Fenton, 5-Feb-2025)

	Ref	Expression
Hypothesis	negsidd.1	$$⊢\phi \to A\in \mathrm{No}$$
Assertion	negsidd	Could not format assertion : No typesetting found for |- ( ph -> ( A +s ( -us ` A ) ) = 0s ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		negsidd.1	$$⊢\phi \to A\in \mathrm{No}$$
2		negsid	Could not format ( A e. No -> ( A +s ( -us ` A ) ) = 0s ) : No typesetting found for |- ( A e. No -> ( A +s ( -us ` A ) ) = 0s ) with typecode |-
3	1 2	syl	Could not format ( ph -> ( A +s ( -us ` A ) ) = 0s ) : No typesetting found for |- ( ph -> ( A +s ( -us ` A ) ) = 0s ) with typecode |-