Axiom ax-0id 8200

Description: 0 is an identity element for real addition. Axiom for real and complex numbers, justified by Theorem ax0id 8158.

Proofs should normally use addrid 8376 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 8090	. . 3 class ℂ
3	1, 2	wcel 2202	. 2 wff 𝐴 ∈ ℂ
4		cc0 8092	. . . 4 class 0
5		caddc 8095	. . . 4 class +
6	1, 4, 5	co 6028	. . 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  8376