Theorem nnne0s

Description: A surreal positive integer is non-zero. (Contributed by Scott Fenton, 15-Apr-2025)

	Ref	Expression
Assertion	nnne0s	⊢ ( 𝐴 ∈ ℕs → 𝐴 ≠ 0s )

Proof

Step	Hyp	Ref	Expression
1		eldifsni	⊢ ( 𝐴 ∈ ( ℕ0s ∖ { 0s } ) → 𝐴 ≠ 0s )
2		df-nns	⊢ ℕs = ( ℕ0s ∖ { 0s } )
3	1 2	eleq2s	⊢ ( 𝐴 ∈ ℕs → 𝐴 ≠ 0s )