Theorem negidd

Description: Addition of a number and its negative. (Contributed by Mario Carneiro, 27-May-2016)

	Ref	Expression
Hypothesis	negidd.1	$$⊢\phi \to A\in ℂ$$
Assertion	negidd	$$⊢\phi \to A+\left(-A\right)=0$$

Proof

Step	Hyp	Ref	Expression
1		negidd.1	$$⊢\phi \to A\in ℂ$$
2		negid	$$⊢A\in ℂ\to A+\left(-A\right)=0$$
3	1 2	syl	$$⊢\phi \to A+\left(-A\right)=0$$