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Theorem times2d 12512
Description: A number times 2. (Contributed by Mario Carneiro, 27-May-2016.)
Hypothesis
Ref Expression
2timesd.1 (𝜑𝐴 ∈ ℂ)
Assertion
Ref Expression
times2d (𝜑 → (𝐴 · 2) = (𝐴 + 𝐴))

Proof of Theorem times2d
StepHypRef Expression
1 2timesd.1 . 2 (𝜑𝐴 ∈ ℂ)
2 times2 12404 . 2 (𝐴 ∈ ℂ → (𝐴 · 2) = (𝐴 + 𝐴))
31, 2syl 17 1 (𝜑 → (𝐴 · 2) = (𝐴 + 𝐴))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1539  wcel 2107  (class class class)co 7432  cc 11154   + caddc 11159   · cmul 11161  2c2 12322
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707  ax-resscn 11213  ax-1cn 11214  ax-icn 11215  ax-addcl 11216  ax-mulcl 11218  ax-mulcom 11220  ax-mulass 11222  ax-distr 11223  ax-1rid 11226  ax-cnre 11229
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1542  df-fal 1552  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-rex 3070  df-rab 3436  df-v 3481  df-dif 3953  df-un 3955  df-ss 3967  df-nul 4333  df-if 4525  df-sn 4626  df-pr 4628  df-op 4632  df-uni 4907  df-br 5143  df-iota 6513  df-fv 6568  df-ov 7435  df-2 12330
This theorem is referenced by:  div4p1lem1div2  12523  climcndslem1  15886  climcndslem2  15887  sadcaddlem  16495  dvexp3  26017  chordthmlem  26876  chordthmlem2  26877  chordthmlem4  26879  logfaclbnd  27267  rplogsumlem1  27529  nexple  32834  aks4d1p1p5  42077  fltne  42659
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