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Mirrors > Home > ILE Home > Th. List > addid2d | GIF version |
Description: 0 is a left identity for addition. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
muld.1 | ⊢ (𝜑 → 𝐴 ∈ ℂ) |
Ref | Expression |
---|---|
addid2d | ⊢ (𝜑 → (0 + 𝐴) = 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | muld.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ ℂ) | |
2 | addid2 7152 | . 2 ⊢ (𝐴 ∈ ℂ → (0 + 𝐴) = 𝐴) | |
3 | 1, 2 | syl 14 | 1 ⊢ (𝜑 → (0 + 𝐴) = 𝐴) |
Colors of variables: wff set class |
Syntax hints: → wi 4 = wceq 1243 ∈ wcel 1393 (class class class)co 5512 ℂcc 6887 0cc0 6889 + caddc 6892 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-17 1419 ax-ial 1427 ax-ext 2022 ax-1cn 6977 ax-icn 6979 ax-addcl 6980 ax-mulcl 6982 ax-addcom 6984 ax-i2m1 6989 ax-0id 6992 |
This theorem depends on definitions: df-bi 110 df-cleq 2033 df-clel 2036 |
This theorem is referenced by: negeu 7202 ltadd2 7416 subge0 7470 sublt0d 7561 un0addcl 8215 lincmb01cmp 8871 rennim 9600 |
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