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Theorem times2d 10143
Description: A number times 2. (Contributed by Mario Carneiro, 27-May-2016.)
Hypothesis
Ref Expression
2timesd.1  |-  ( ph  ->  A  e.  CC )
Assertion
Ref Expression
times2d  |-  ( ph  ->  ( A  x.  2 )  =  ( A  +  A ) )

Proof of Theorem times2d
StepHypRef Expression
1 2timesd.1 . 2  |-  ( ph  ->  A  e.  CC )
2 times2 10032 . 2  |-  ( A  e.  CC  ->  ( A  x.  2 )  =  ( A  +  A ) )
31, 2syl 16 1  |-  ( ph  ->  ( A  x.  2 )  =  ( A  +  A ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1649    e. wcel 1717  (class class class)co 6020   CCcc 8921    + caddc 8926    x. cmul 8928   2c2 9981
This theorem is referenced by:  climcndslem1  12556  climcndslem2  12557  sadcaddlem  12896  dvexp3  19729  chordthmlem  20540  chordthmlem2  20541  chordthmlem4  20543  logfaclbnd  20873  rplogsumlem1  21045
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368  ax-resscn 8980  ax-1cn 8981  ax-icn 8982  ax-addcl 8983  ax-addrcl 8984  ax-mulcl 8985  ax-mulrcl 8986  ax-mulcom 8987  ax-mulass 8989  ax-distr 8990  ax-i2m1 8991  ax-1ne0 8992  ax-1rid 8993  ax-rrecex 8995  ax-cnre 8996
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-ne 2552  df-ral 2654  df-rex 2655  df-rab 2658  df-v 2901  df-dif 3266  df-un 3268  df-in 3270  df-ss 3277  df-nul 3572  df-if 3683  df-sn 3763  df-pr 3764  df-op 3766  df-uni 3958  df-br 4154  df-iota 5358  df-fv 5402  df-ov 6023  df-2 9990
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