Axiom ax-0id 8075

Description: 0 is an identity element for real addition. Axiom for real and complex numbers, justified by Theorem ax0id 8033.

Proofs should normally use addrid 8252 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 7965	. . 3 class ℂ
3	1, 2	wcel 2180	. 2 wff 𝐴 ∈ ℂ
4		cc0 7967	. . . 4 class 0
5		caddc 7970	. . . 4 class +
6	1, 4, 5	co 5974	. . 3 class (𝐴 + 0)
7	6, 1	wceq 1375	. 2 wff (𝐴 + 0) = 𝐴
8	3, 7	wi 4	1 wff (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)

This axiom is referenced by:  addrid  8252