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Mirrors > Home > ILE Home > Th. List > addid2i | GIF version |
Description: 0 is a left identity for addition. (Contributed by NM, 3-Jan-2013.) |
Ref | Expression |
---|---|
mul.1 | ⊢ 𝐴 ∈ ℂ |
Ref | Expression |
---|---|
addid2i | ⊢ (0 + 𝐴) = 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mul.1 | . 2 ⊢ 𝐴 ∈ ℂ | |
2 | addid2 7152 | . 2 ⊢ (𝐴 ∈ ℂ → (0 + 𝐴) = 𝐴) | |
3 | 1, 2 | ax-mp 7 | 1 ⊢ (0 + 𝐴) = 𝐴 |
Colors of variables: wff set class |
Syntax hints: = 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: ine0 7391 inelr 7575 muleqadd 7649 0p1e1 8031 iap0 8148 num0h 8377 nummul1c 8403 fz0tp 8981 fzo0to3tp 9075 rei 9499 imi 9500 resqrexlemover 9608 |
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