Axiom ax-0id 7084

Description: 0 is an identity element for real addition. Axiom for real and complex numbers, justified by theorem ax0id 7044.

Proofs should normally use addid1 7246 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 6979	. . 3 class ℂ
3	1, 2	wcel 1433	. 2 wff 𝐴 ∈ ℂ
4		cc0 6981	. . . 4 class 0
5		caddc 6984	. . . 4 class +
6	1, 4, 5	co 5532	. . 3 class (𝐴 + 0)
7	6, 1	wceq 1284	. 2 wff (𝐴 + 0) = 𝐴
8	3, 7	wi 4	1 wff (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)

This axiom is referenced by:  addid1  7246