Theorem negsf

Description: Function statement for surreal negation. (Contributed by Scott Fenton, 3-Feb-2025)

	Ref	Expression
Assertion	negsf	$$⊢{+}_s:\mathrm{No}⟶\mathrm{No}$$

Proof

Step	Hyp	Ref	Expression
1		negsfn	$$⊢{+}_{s}Fn\mathrm{No}$$
2		negscl	$$⊢x\in \mathrm{No}\to {+}_s\left(x\right)\in \mathrm{No}$$
3	2	rgen	$$⊢\forall x\in \mathrm{No}{+}_s\left(x\right)\in \mathrm{No}$$
4		ffnfv	$$⊢{+}_s:\mathrm{No}⟶\mathrm{No}\leftrightarrow \left({+}_{s}Fn\mathrm{No}\wedge \forall x\in \mathrm{No}{+}_s\left(x\right)\in \mathrm{No}\right)$$
5	1 3 4	mpbir2an	$$⊢{+}_s:\mathrm{No}⟶\mathrm{No}$$