Axiom ax-0id 8140

Description: 0 is an identity element for real addition. Axiom for real and complex numbers, justified by Theorem ax0id 8098.

Proofs should normally use addrid 8317 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 8030	. . 3 class ℂ
3	1, 2	wcel 2202	. 2 wff 𝐴 ∈ ℂ
4		cc0 8032	. . . 4 class 0
5		caddc 8035	. . . 4 class +
6	1, 4, 5	co 6018	. . 3 class (𝐴 + 0)
7	6, 1	wceq 1397	. 2 wff (𝐴 + 0) = 𝐴
8	3, 7	wi 4	1 wff (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)

This axiom is referenced by:  addrid  8317