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Axiom ax-0id 7918
Description: 0 is an identity element for real addition. Axiom for real and complex numbers, justified by Theorem ax0id 7876.

Proofs should normally use addid1 8093 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
StepHypRef Expression
1 cA . . 3 class 𝐴
2 cc 7808 . . 3 class
31, 2wcel 2148 . 2 wff 𝐴 ∈ ℂ
4 cc0 7810 . . . 4 class 0
5 caddc 7813 . . . 4 class +
61, 4, 5co 5874 . . 3 class (𝐴 + 0)
76, 1wceq 1353 . 2 wff (𝐴 + 0) = 𝐴
83, 7wi 4 1 wff (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴)
Colors of variables: wff set class
This axiom is referenced by:  addid1  8093
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