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Mirrors > Home > ILE Home > Th. List > ax-0id | GIF version |
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.) |
Ref | Expression |
---|---|
ax-0id | ⊢ (𝐴 ∈ ℂ → (𝐴 + 0) = 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 class 𝐴 | |
2 | cc 7586 | . . 3 class ℂ | |
3 | 1, 2 | wcel 1465 | . 2 wff 𝐴 ∈ ℂ |
4 | cc0 7588 | . . . 4 class 0 | |
5 | caddc 7591 | . . . 4 class + | |
6 | 1, 4, 5 | co 5742 | . . 3 class (𝐴 + 0) |
7 | 6, 1 | wceq 1316 | . 2 wff (𝐴 + 0) = 𝐴 |
8 | 3, 7 | wi 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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