Axiom ax-0id 7980

Description: 0 is an identity element for real addition. Axiom for real and complex numbers, justified by Theorem ax0id 7938.

Proofs should normally use addrid 8157 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 7870	. . 3 class ℂ
3	1, 2	wcel 2164	. 2 wff 𝐴 ∈ ℂ
4		cc0 7872	. . . 4 class 0
5		caddc 7875	. . . 4 class +
6	1, 4, 5	co 5918	. . 3 class (𝐴 + 0)
7	6, 1	wceq 1364	. 2 wff (𝐴 + 0) = 𝐴
8	3, 7	wi 4	1 wff (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)

This axiom is referenced by:  addrid  8157