Axiom ax-0id 8115

Description: 0 is an identity element for real addition. Axiom for real and complex numbers, justified by Theorem ax0id 8073.

Proofs should normally use addrid 8292 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 8005	. . 3 class ℂ
3	1, 2	wcel 2200	. 2 wff 𝐴 ∈ ℂ
4		cc0 8007	. . . 4 class 0
5		caddc 8010	. . . 4 class +
6	1, 4, 5	co 6007	. . 3 class (𝐴 + 0)
7	6, 1	wceq 1395	. 2 wff (𝐴 + 0) = 𝐴
8	3, 7	wi 4	1 wff (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)

This axiom is referenced by:  addrid  8292