Axiom ax-0id 7861

Description: 0 is an identity element for real addition. Axiom for real and complex numbers, justified by Theorem ax0id 7819.

Proofs should normally use addid1 8036 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 7751	. . 3 class ℂ
3	1, 2	wcel 2136	. 2 wff 𝐴 ∈ ℂ
4		cc0 7753	. . . 4 class 0
5		caddc 7756	. . . 4 class +
6	1, 4, 5	co 5842	. . 3 class (𝐴 + 0)
7	6, 1	wceq 1343	. 2 wff (𝐴 + 0) = 𝐴
8	3, 7	wi 4	1 wff (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)

This axiom is referenced by:  addid1  8036