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Axiom ax-0id 7050
Description: 0 is an identity element for real addition. Axiom for real and complex numbers, justified by theorem ax0id 7010.

Proofs should normally use addid1 7212 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 6945 . . 3 class
31, 2wcel 1409 . 2 wff 𝐴 ∈ ℂ
4 cc0 6947 . . . 4 class 0
5 caddc 6950 . . . 4 class +
61, 4, 5co 5540 . . 3 class (𝐴 + 0)
76, 1wceq 1259 . 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  7212
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