Axiom ax-0id 8006

Description: 0 is an identity element for real addition. Axiom for real and complex numbers, justified by Theorem ax0id 7964.

Proofs should normally use addrid 8183 instead. (New usage is discouraged.) (Contributed by Jim Kingdon, 16-Jan-2020.)

Assertion

Ref	Expression
ax-0id	⊢ (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)

Detailed syntax breakdown of Axiom ax-0id

Step	Hyp	Ref	Expression
1		cA	. . 3 class 𝐴
2		cc 7896	. . 3 class ℂ
3	1, 2	wcel 2167	. 2 wff 𝐴 ∈ ℂ
4		cc0 7898	. . . 4 class 0
5		caddc 7901	. . . 4 class +
6	1, 4, 5	co 5925	. . 3 class (𝐴 + 0)
7	6, 1	wceq 1364	. 2 wff (𝐴 + 0) = 𝐴
8	3, 7	wi 4	1 wff (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)

This axiom is referenced by:  addrid  8183