Axiom ax-0id 8237

Description: 0 is an identity element for real addition. Axiom for real and complex numbers, justified by Theorem ax0id 8195.

Proofs should normally use addrid 8413 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 8127	. . 3 class ℂ
3	1, 2	wcel 2205	. 2 wff 𝐴 ∈ ℂ
4		cc0 8129	. . . 4 class 0
5		caddc 8132	. . . 4 class +
6	1, 4, 5	co 6052	. . 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  8413