Theorem negcld

Description: Closure law for negative. (Contributed by Mario Carneiro, 27-May-2016)

	Ref	Expression
Hypothesis	negidd.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
Assertion	negcld	⊢ ( 𝜑 → - 𝐴 ∈ ℂ )

Proof

Step	Hyp	Ref	Expression
1		negidd.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
2		negcl	⊢ ( 𝐴 ∈ ℂ → - 𝐴 ∈ ℂ )
3	1 2	syl	⊢ ( 𝜑 → - 𝐴 ∈ ℂ )