Theorem negsf

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

	Ref	Expression
Assertion	negsf	⊢ -us : No ⟶ No

Proof

Step	Hyp	Ref	Expression
1		negsfn	⊢ -us Fn No
2		negscl	⊢ ( 𝑥 ∈ No → ( -us ‘ 𝑥 ) ∈ No )
3	2	rgen	⊢ ∀ 𝑥 ∈ No ( -us ‘ 𝑥 ) ∈ No
4		ffnfv	⊢ ( -us : No ⟶ No ↔ ( -us Fn No ∧ ∀ 𝑥 ∈ No ( -us ‘ 𝑥 ) ∈ No ) )
5	1 3 4	mpbir2an	⊢ -us : No ⟶ No