Axiom ax-0id 7921

Description: 0 is an identity element for real addition. Axiom for real and complex numbers, justified by Theorem ax0id 7879.

Proofs should normally use addid1 8097 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 7811	. . 3 class ℂ
3	1, 2	wcel 2148	. 2 wff 𝐴 ∈ ℂ
4		cc0 7813	. . . 4 class 0
5		caddc 7816	. . . 4 class +
6	1, 4, 5	co 5877	. . 3 class (𝐴 + 0)
7	6, 1	wceq 1353	. 2 wff (𝐴 + 0) = 𝐴
8	3, 7	wi 4	1 wff (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)

This axiom is referenced by:  addid1  8097