Axiom ax-0id 7987

Description: 0 is an identity element for real addition. Axiom for real and complex numbers, justified by Theorem ax0id 7945.

Proofs should normally use addrid 8164 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 7877	. . 3 class ℂ
3	1, 2	wcel 2167	. 2 wff 𝐴 ∈ ℂ
4		cc0 7879	. . . 4 class 0
5		caddc 7882	. . . 4 class +
6	1, 4, 5	co 5922	. . 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  8164