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Mirrors > Home > ILE Home > Th. List > times2i | GIF version |
Description: A number times 2. (Contributed by NM, 11-May-2004.) |
Ref | Expression |
---|---|
2times.1 | ⊢ 𝐴 ∈ ℂ |
Ref | Expression |
---|---|
times2i | ⊢ (𝐴 · 2) = (𝐴 + 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2times.1 | . 2 ⊢ 𝐴 ∈ ℂ | |
2 | times2 9062 | . 2 ⊢ (𝐴 ∈ ℂ → (𝐴 · 2) = (𝐴 + 𝐴)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝐴 · 2) = (𝐴 + 𝐴) |
Colors of variables: wff set class |
Syntax hints: = wceq 1363 ∈ wcel 2158 (class class class)co 5888 ℂcc 7823 + caddc 7828 · cmul 7830 2c2 8984 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2169 ax-resscn 7917 ax-1cn 7918 ax-1re 7919 ax-icn 7920 ax-addcl 7921 ax-addrcl 7922 ax-mulcl 7923 ax-mulcom 7926 ax-mulass 7928 ax-distr 7929 ax-1rid 7932 ax-cnre 7936 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-nf 1471 df-sb 1773 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-ral 2470 df-rex 2471 df-v 2751 df-un 3145 df-in 3147 df-ss 3154 df-sn 3610 df-pr 3611 df-op 3613 df-uni 3822 df-br 4016 df-iota 5190 df-fv 5236 df-ov 5891 df-2 8992 |
This theorem is referenced by: 3t2e6 9089 4t2e8 9091 6t2e12 9501 7t2e14 9506 8t2e16 9512 9t2e18 9519 |
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