Theorem lt0ne0

Description: A number which is less than zero is not zero. (Contributed by Stefan O'Rear, 13-Sep-2014)

	Ref	Expression
Assertion	lt0ne0	⊢ ( ( 𝐴 ∈ ℝ ∧ 𝐴 < 0 ) → 𝐴 ≠ 0 )

Proof

Step	Hyp	Ref	Expression
1		ltne	⊢ ( ( 𝐴 ∈ ℝ ∧ 𝐴 < 0 ) → 0 ≠ 𝐴 )
2	1	necomd	⊢ ( ( 𝐴 ∈ ℝ ∧ 𝐴 < 0 ) → 𝐴 ≠ 0 )