Axiom ax-0id 8128

Description: 0 is an identity element for real addition. Axiom for real and complex numbers, justified by Theorem ax0id 8086.

Proofs should normally use addrid 8305 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 8018	. . 3 class ℂ
3	1, 2	wcel 2200	. 2 wff 𝐴 ∈ ℂ
4		cc0 8020	. . . 4 class 0
5		caddc 8023	. . . 4 class +
6	1, 4, 5	co 6011	. . 3 class (𝐴 + 0)
7	6, 1	wceq 1395	. 2 wff (𝐴 + 0) = 𝐴
8	3, 7	wi 4	1 wff (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)

This axiom is referenced by:  addrid  8305