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Theorem 6p3e9 12426
Description: 6 + 3 = 9. (Contributed by NM, 11-May-2004.)
Assertion
Ref Expression
6p3e9 (6 + 3) = 9

Proof of Theorem 6p3e9
StepHypRef Expression
1 df-3 12330 . . . 4 3 = (2 + 1)
21oveq2i 7442 . . 3 (6 + 3) = (6 + (2 + 1))
3 6cn 12357 . . . 4 6 ∈ ℂ
4 2cn 12341 . . . 4 2 ∈ ℂ
5 ax-1cn 11213 . . . 4 1 ∈ ℂ
63, 4, 5addassi 11271 . . 3 ((6 + 2) + 1) = (6 + (2 + 1))
72, 6eqtr4i 2768 . 2 (6 + 3) = ((6 + 2) + 1)
8 df-9 12336 . . 3 9 = (8 + 1)
9 6p2e8 12425 . . . 4 (6 + 2) = 8
109oveq1i 7441 . . 3 ((6 + 2) + 1) = (8 + 1)
118, 10eqtr4i 2768 . 2 9 = ((6 + 2) + 1)
127, 11eqtr4i 2768 1 (6 + 3) = 9
Colors of variables: wff setvar class
Syntax hints:   = wceq 1540  (class class class)co 7431  1c1 11156   + caddc 11158  2c2 12321  3c3 12322  6c6 12325  8c8 12327  9c9 12328
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708  ax-1cn 11213  ax-addcl 11215  ax-addass 11220
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-rab 3437  df-v 3482  df-dif 3954  df-un 3956  df-ss 3968  df-nul 4334  df-if 4526  df-sn 4627  df-pr 4629  df-op 4633  df-uni 4908  df-br 5144  df-iota 6514  df-fv 6569  df-ov 7434  df-2 12329  df-3 12330  df-4 12331  df-5 12332  df-6 12333  df-7 12334  df-8 12335  df-9 12336
This theorem is referenced by:  3t3e9  12433  6p4e10  12805  2exp8  17126  139prm  17161  2503lem2  17175  4001lem1  17178  4001lem2  17179  4001lem4  17181  log2ublem3  26991  ex-gcd  30476  hgt750lem2  34667  kur14lem8  35218  problem5  35674  fmtno5lem1  47540  139prmALT  47583  gboge9  47751  gbpart9  47756  nnsum4primeseven  47787
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