Axiom ax-0id 8293

Description: 0 is an identity element for real addition. Axiom for real and complex numbers, justified by Theorem ax0id 8251.

Proofs should normally use addrid 8471 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 8183	. . 3 class ℂ
3	1, 2	wcel 2209	. 2 wff 𝐴 ∈ ℂ
4		cc0 8185	. . . 4 class 0
5		caddc 8188	. . . 4 class +
6	1, 4, 5	co 6088	. . 3 class (𝐴 + 0)
7	6, 1	wceq 1402	. 2 wff (𝐴 + 0) = 𝐴
8	3, 7	wi 4	1 wff (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)

This axiom is used by:  addrid  8471