MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  times2i Unicode version

Theorem times2i 9938
Description: A number times 2. (Contributed by NM, 11-May-2004.)
Hypothesis
Ref Expression
2times.1  |-  A  e.  CC
Assertion
Ref Expression
times2i  |-  ( A  x.  2 )  =  ( A  +  A
)

Proof of Theorem times2i
StepHypRef Expression
1 2times.1 . 2  |-  A  e.  CC
2 times2 9936 . 2  |-  ( A  e.  CC  ->  ( A  x.  2 )  =  ( A  +  A ) )
31, 2ax-mp 8 1  |-  ( A  x.  2 )  =  ( A  +  A
)
Colors of variables: wff set class
Syntax hints:    = wceq 1642    e. wcel 1710  (class class class)co 5945   CCcc 8825    + caddc 8830    x. cmul 8832   2c2 9885
This theorem is referenced by:  3t2e6  9964  4t2e8  9966  5t2e10  9967  6t2e12  10293  7t2e14  10298  8t2e16  10304  9t2e18  10311
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339  ax-resscn 8884  ax-1cn 8885  ax-icn 8886  ax-addcl 8887  ax-addrcl 8888  ax-mulcl 8889  ax-mulrcl 8890  ax-mulcom 8891  ax-mulass 8893  ax-distr 8894  ax-i2m1 8895  ax-1ne0 8896  ax-1rid 8897  ax-rrecex 8899  ax-cnre 8900
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-ne 2523  df-ral 2624  df-rex 2625  df-rab 2628  df-v 2866  df-dif 3231  df-un 3233  df-in 3235  df-ss 3242  df-nul 3532  df-if 3642  df-sn 3722  df-pr 3723  df-op 3725  df-uni 3909  df-br 4105  df-iota 5301  df-fv 5345  df-ov 5948  df-2 9894
  Copyright terms: Public domain W3C validator