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Theorem times2d 10203
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 10092 . 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 1652    e. wcel 1725  (class class class)co 6073   CCcc 8980    + caddc 8985    x. cmul 8987   2c2 10041
This theorem is referenced by:  climcndslem1  12621  climcndslem2  12622  sadcaddlem  12961  dvexp3  19854  chordthmlem  20665  chordthmlem2  20666  chordthmlem4  20668  logfaclbnd  20998  rplogsumlem1  21170
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-resscn 9039  ax-1cn 9040  ax-icn 9041  ax-addcl 9042  ax-addrcl 9043  ax-mulcl 9044  ax-mulrcl 9045  ax-mulcom 9046  ax-mulass 9048  ax-distr 9049  ax-i2m1 9050  ax-1ne0 9051  ax-1rid 9052  ax-rrecex 9054  ax-cnre 9055
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-iota 5410  df-fv 5454  df-ov 6076  df-2 10050
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