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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 8643 | . 2 ⊢ (𝐴 ∈ ℂ → (𝐴 · 2) = (𝐴 + 𝐴)) | |
3 | 1, 2 | ax-mp 7 | 1 ⊢ (𝐴 · 2) = (𝐴 + 𝐴) |
Colors of variables: wff set class |
Syntax hints: = wceq 1296 ∈ wcel 1445 (class class class)co 5690 ℂcc 7445 + caddc 7450 · cmul 7452 2c2 8571 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 ax-resscn 7534 ax-1cn 7535 ax-1re 7536 ax-icn 7537 ax-addcl 7538 ax-addrcl 7539 ax-mulcl 7540 ax-mulcom 7543 ax-mulass 7545 ax-distr 7546 ax-1rid 7549 ax-cnre 7553 |
This theorem depends on definitions: df-bi 116 df-3an 929 df-tru 1299 df-nf 1402 df-sb 1700 df-clab 2082 df-cleq 2088 df-clel 2091 df-nfc 2224 df-ral 2375 df-rex 2376 df-v 2635 df-un 3017 df-in 3019 df-ss 3026 df-sn 3472 df-pr 3473 df-op 3475 df-uni 3676 df-br 3868 df-iota 5014 df-fv 5057 df-ov 5693 df-2 8579 |
This theorem is referenced by: 3t2e6 8670 4t2e8 8672 6t2e12 9079 7t2e14 9084 8t2e16 9090 9t2e18 9097 |
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