Axiom ax-0id 8251

Description: 0 is an identity element for real addition. Axiom for real and complex numbers, justified by Theorem ax0id 8209.

Proofs should normally use addrid 8427 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 8141	. . 3 class ℂ
3	1, 2	wcel 2205	. 2 wff 𝐴 ∈ ℂ
4		cc0 8143	. . . 4 class 0
5		caddc 8146	. . . 4 class +
6	1, 4, 5	co 6058	. . 3 class (𝐴 + 0)
7	6, 1	wceq 1398	. 2 wff (𝐴 + 0) = 𝐴
8	3, 7	wi 4	1 wff (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)

This axiom is referenced by:  addrid  8427