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Theorem times2d 9076
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 8962 . 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 1335    e. wcel 2128  (class class class)co 5824   CCcc 7730    + caddc 7735    x. cmul 7737   2c2 8884
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139  ax-resscn 7824  ax-1cn 7825  ax-1re 7826  ax-icn 7827  ax-addcl 7828  ax-addrcl 7829  ax-mulcl 7830  ax-mulcom 7833  ax-mulass 7835  ax-distr 7836  ax-1rid 7839  ax-cnre 7843
This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-ral 2440  df-rex 2441  df-v 2714  df-un 3106  df-in 3108  df-ss 3115  df-sn 3566  df-pr 3567  df-op 3569  df-uni 3773  df-br 3966  df-iota 5135  df-fv 5178  df-ov 5827  df-2 8892
This theorem is referenced by:  div4p1lem1div2  9086
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