Axiom ax-0id 8280

Description: 0 is an identity element for real addition. Axiom for real and complex numbers, justified by Theorem ax0id 8238.

Proofs should normally use addrid 8457 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 8170	. . 3 class ℂ
3	1, 2	wcel 2209	. 2 wff 𝐴 ∈ ℂ
4		cc0 8172	. . . 4 class 0
5		caddc 8175	. . . 4 class +
6	1, 4, 5	co 6078	. . 3 class (𝐴 + 0)
7	6, 1	wceq 1402	. 2 wff (𝐴 + 0) = 𝐴
8	3, 7	wi 4	1 wff (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)

This axiom is referenced by:  addrid  8457