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Theorem times2d 10672
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 10545 . 2  |-  ( A  e.  CC  ->  ( A  x.  2 )  =  ( A  +  A ) )
31, 2syl 16 1  |-  ( ph  ->  ( A  x.  2 )  =  ( A  +  A ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1370    e. wcel 1758  (class class class)co 6193   CCcc 9384    + caddc 9389    x. cmul 9391   2c2 10475
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-ext 2430  ax-resscn 9443  ax-1cn 9444  ax-icn 9445  ax-addcl 9446  ax-addrcl 9447  ax-mulcl 9448  ax-mulrcl 9449  ax-mulcom 9450  ax-mulass 9452  ax-distr 9453  ax-i2m1 9454  ax-1ne0 9455  ax-1rid 9456  ax-rrecex 9458  ax-cnre 9459
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2601  df-ne 2646  df-ral 2800  df-rex 2801  df-rab 2804  df-v 3073  df-dif 3432  df-un 3434  df-in 3436  df-ss 3443  df-nul 3739  df-if 3893  df-sn 3979  df-pr 3981  df-op 3985  df-uni 4193  df-br 4394  df-iota 5482  df-fv 5527  df-ov 6196  df-2 10484
This theorem is referenced by:  climcndslem1  13423  climcndslem2  13424  sadcaddlem  13764  dvexp3  21576  chordthmlem  22353  chordthmlem2  22354  chordthmlem4  22356  logfaclbnd  22687  rplogsumlem1  22859  nexple  26586
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