Axiom ax-0id 8040

Description: 0 is an identity element for real addition. Axiom for real and complex numbers, justified by Theorem ax0id 7998.

Proofs should normally use addrid 8217 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 7930	. . 3 class ℂ
3	1, 2	wcel 2177	. 2 wff 𝐴 ∈ ℂ
4		cc0 7932	. . . 4 class 0
5		caddc 7935	. . . 4 class +
6	1, 4, 5	co 5951	. . 3 class (𝐴 + 0)
7	6, 1	wceq 1373	. 2 wff (𝐴 + 0) = 𝐴
8	3, 7	wi 4	1 wff (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)

This axiom is referenced by:  addrid  8217