Theorem negnegd

Description: A number is equal to the negative of its negative. Theorem I.4 of Apostol p. 18. (Contributed by Mario Carneiro, 27-May-2016)

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

Proof

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