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Theorem 6p3e9 12371
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 12275 . . . 4 3 = (2 + 1)
21oveq2i 7413 . . 3 (6 + 3) = (6 + (2 + 1))
3 6cn 12302 . . . 4 6 ∈ ℂ
4 2cn 12286 . . . 4 2 ∈ ℂ
5 ax-1cn 11165 . . . 4 1 ∈ ℂ
63, 4, 5addassi 11223 . . 3 ((6 + 2) + 1) = (6 + (2 + 1))
72, 6eqtr4i 2755 . 2 (6 + 3) = ((6 + 2) + 1)
8 df-9 12281 . . 3 9 = (8 + 1)
9 6p2e8 12370 . . . 4 (6 + 2) = 8
109oveq1i 7412 . . 3 ((6 + 2) + 1) = (8 + 1)
118, 10eqtr4i 2755 . 2 9 = ((6 + 2) + 1)
127, 11eqtr4i 2755 1 (6 + 3) = 9
Colors of variables: wff setvar class
Syntax hints:   = wceq 1533  (class class class)co 7402  1c1 11108   + caddc 11110  2c2 12266  3c3 12267  6c6 12270  8c8 12272  9c9 12273
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695  ax-1cn 11165  ax-addcl 11167  ax-addass 11172
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-rab 3425  df-v 3468  df-dif 3944  df-un 3946  df-in 3948  df-ss 3958  df-nul 4316  df-if 4522  df-sn 4622  df-pr 4624  df-op 4628  df-uni 4901  df-br 5140  df-iota 6486  df-fv 6542  df-ov 7405  df-2 12274  df-3 12275  df-4 12276  df-5 12277  df-6 12278  df-7 12279  df-8 12280  df-9 12281
This theorem is referenced by:  3t3e9  12378  6p4e10  12748  2exp8  17027  139prm  17062  2503lem2  17076  4001lem1  17079  4001lem2  17080  4001lem4  17082  log2ublem3  26820  ex-gcd  30204  hgt750lem2  34182  kur14lem8  34721  problem5  35171  fmtno5lem1  46766  139prmALT  46809  gboge9  46977  gbpart9  46982  nnsum4primeseven  47013
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