Theorem half0

Description: Half of a number is zero iff the number is zero. (Contributed by NM, 20-Apr-2006)

	Ref	Expression
Assertion	half0	⊢ ( 𝐴 ∈ ℂ → ( ( 𝐴 / 2 ) = 0 ↔ 𝐴 = 0 ) )

Proof

Step	Hyp	Ref	Expression
1		2cn	⊢ 2 ∈ ℂ
2		2ne0	⊢ 2 ≠ 0
3		diveq0	⊢ ( ( 𝐴 ∈ ℂ ∧ 2 ∈ ℂ ∧ 2 ≠ 0 ) → ( ( 𝐴 / 2 ) = 0 ↔ 𝐴 = 0 ) )
4	1 2 3	mp3an23	⊢ ( 𝐴 ∈ ℂ → ( ( 𝐴 / 2 ) = 0 ↔ 𝐴 = 0 ) )