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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 7810.
Proofs should normally use addid1 8027 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 7742 | . . 3 class ℂ | |
3 | 1, 2 | wcel 2135 | . 2 wff 𝐴 ∈ ℂ |
4 | cc0 7744 | . . . 4 class 0 | |
5 | caddc 7747 | . . . 4 class + | |
6 | 1, 4, 5 | co 5836 | . . 3 class (𝐴 + 0) |
7 | 6, 1 | wceq 1342 | . 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 8027 |
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