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Axiom ax-0id 7696
Description: 0 is an identity element for real addition. Axiom for real and complex numbers, justified by theorem ax0id 7654.

Proofs should normally use addid1 7868 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 7586 . . 3 class
31, 2wcel 1465 . 2 wff 𝐴 ∈ ℂ
4 cc0 7588 . . . 4 class 0
5 caddc 7591 . . . 4 class +
61, 4, 5co 5742 . . 3 class (𝐴 + 0)
76, 1wceq 1316 . 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  7868
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