Axiom ax-0id 6992

Description: 0 is an identity element for real addition. Axiom for real and complex numbers, justified by theorem ax0id 6952.

Proofs should normally use addid1 7151 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 6887	. . 3 class ℂ
3	1, 2	wcel 1393	. 2 wff 𝐴 ∈ ℂ
4		cc0 6889	. . . 4 class 0
5		caddc 6892	. . . 4 class +
6	1, 4, 5	co 5512	. . 3 class (𝐴 + 0)
7	6, 1	wceq 1243	. 2 wff (𝐴 + 0) = 𝐴
8	3, 7	wi 4	1 wff (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)

This axiom is referenced by:  addid1  7151