Axiom ax-0id 7603

Description: 0 is an identity element for real addition. Axiom for real and complex numbers, justified by theorem ax0id 7563.

Proofs should normally use addid1 7771 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 7498	. . 3 class ℂ
3	1, 2	wcel 1448	. 2 wff 𝐴 ∈ ℂ
4		cc0 7500	. . . 4 class 0
5		caddc 7503	. . . 4 class +
6	1, 4, 5	co 5706	. . 3 class (𝐴 + 0)
7	6, 1	wceq 1299	. 2 wff (𝐴 + 0) = 𝐴
8	3, 7	wi 4	1 wff (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)

This axiom is referenced by:  addid1  7771