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Theorem times2d 9192
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 9078 . 2  |-  ( A  e.  CC  ->  ( A  x.  2 )  =  ( A  +  A ) )
31, 2syl 14 1  |-  ( ph  ->  ( A  x.  2 )  =  ( A  +  A ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1364    e. wcel 2160  (class class class)co 5896   CCcc 7839    + caddc 7844    x. cmul 7846   2c2 9000
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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171  ax-resscn 7933  ax-1cn 7934  ax-1re 7935  ax-icn 7936  ax-addcl 7937  ax-addrcl 7938  ax-mulcl 7939  ax-mulcom 7942  ax-mulass 7944  ax-distr 7945  ax-1rid 7948  ax-cnre 7952
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-ral 2473  df-rex 2474  df-v 2754  df-un 3148  df-in 3150  df-ss 3157  df-sn 3613  df-pr 3614  df-op 3616  df-uni 3825  df-br 4019  df-iota 5196  df-fv 5243  df-ov 5899  df-2 9008
This theorem is referenced by:  div4p1lem1div2  9202
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