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Axiom ax-0id 6990
Description: 0 is an identity element for real addition. Axiom for real and complex numbers, justified by theorem ax0id 6950.

Proofs should normally use addid1 7149 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 6885 . . 3 class
31, 2wcel 1393 . 2 wff 𝐴 ∈ ℂ
4 cc0 6887 . . . 4 class 0
5 caddc 6890 . . . 4 class +
61, 4, 5co 5512 . . 3 class (𝐴 + 0)
76, 1wceq 1243 . 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  7149
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