Theorem negidd

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

	Ref	Expression
Hypothesis	negidd.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
Assertion	negidd	⊢ ( 𝜑 → ( 𝐴 + - 𝐴 ) = 0 )

Proof

Step	Hyp	Ref	Expression
1		negidd.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
2		negid	⊢ ( 𝐴 ∈ ℂ → ( 𝐴 + - 𝐴 ) = 0 )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐴 + - 𝐴 ) = 0 )