Theorem xneg0

Description: The negative of zero. (Contributed by Mario Carneiro, 20-Aug-2015)

	Ref	Expression
Assertion	xneg0	⊢ -𝑒 0 = 0

Proof

Step	Hyp	Ref	Expression
1		0re	⊢ 0 ∈ ℝ
2		rexneg	⊢ ( 0 ∈ ℝ → -𝑒 0 = - 0 )
3	1 2	ax-mp	⊢ -𝑒 0 = - 0
4		neg0	⊢ - 0 = 0
5	3 4	eqtri	⊢ -𝑒 0 = 0