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| Mirrors > Home > MPE Home > Th. List > times2i | Structured version Visualization version GIF version | ||
| Description: A number times 2. (Contributed by NM, 11-May-2004.) |
| Ref | Expression |
|---|---|
| 2timesi.1 | ⊢ 𝐴 ∈ ℂ |
| Ref | Expression |
|---|---|
| times2i | ⊢ (𝐴 · 2) = (𝐴 + 𝐴) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 2timesi.1 | . 2 ⊢ 𝐴 ∈ ℂ | |
| 2 | times2 12340 | . 2 ⊢ (𝐴 ∈ ℂ → (𝐴 · 2) = (𝐴 + 𝐴)) | |
| 3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝐴 · 2) = (𝐴 + 𝐴) |
| Colors of variables: wff setvar class |
| Syntax hints: = wceq 1550 ∈ wcel 2132 (class class class)co 7381 ℂcc 11057 + caddc 11062 · cmul 11064 2c2 12258 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1805 ax-4 1819 ax-5 1920 ax-6 1977 ax-7 2018 ax-8 2134 ax-9 2142 ax-ext 2724 ax-resscn 11116 ax-1cn 11117 ax-icn 11118 ax-addcl 11119 ax-mulcl 11121 ax-mulcom 11123 ax-mulass 11125 ax-distr 11126 ax-1rid 11129 ax-cnre 11132 |
| This theorem depends on definitions: df-bi 209 df-an 399 df-or 857 df-3an 1097 df-tru 1553 df-fal 1563 df-ex 1790 df-sb 2081 df-clab 2731 df-cleq 2744 df-clel 2827 df-rex 3077 df-rab 3405 df-v 3446 df-dif 3898 df-un 3900 df-ss 3912 df-nul 4277 df-if 4471 df-sn 4573 df-pr 4575 df-op 4579 df-uni 4856 df-br 5091 df-iota 6462 df-fv 6514 df-ov 7384 df-2 12266 |
| This theorem is referenced by: 3t2e6 12369 4t2e8 12372 6t2e12 12783 7t2e14 12788 8t2e16 12794 9t2e18 12801 logi 26618 threehalves 33042 areaquad 43731 |
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