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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 7247 | . 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 1284 ∈ wcel 1433 (class class class)co 5532 ℂcc 6979 0cc0 6981 + caddc 6984 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-4 1440 ax-17 1459 ax-ial 1467 ax-ext 2063 ax-1cn 7069 ax-icn 7071 ax-addcl 7072 ax-mulcl 7074 ax-addcom 7076 ax-i2m1 7081 ax-0id 7084 |
This theorem depends on definitions: df-bi 115 df-cleq 2074 df-clel 2077 |
This theorem is referenced by: negeu 7299 ltadd2 7523 subge0 7579 sublt0d 7670 un0addcl 8321 lincmb01cmp 9025 modsumfzodifsn 9398 rennim 9888 max0addsup 10105 moddvds 10204 gcdaddm 10375 bezoutlemb 10389 |
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