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Theorem 6p3e9 12320
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 12224 . . . 4 3 = (2 + 1)
21oveq2i 7373 . . 3 (6 + 3) = (6 + (2 + 1))
3 6cn 12251 . . . 4 6 ∈ ℂ
4 2cn 12235 . . . 4 2 ∈ ℂ
5 ax-1cn 11116 . . . 4 1 ∈ ℂ
63, 4, 5addassi 11172 . . 3 ((6 + 2) + 1) = (6 + (2 + 1))
72, 6eqtr4i 2768 . 2 (6 + 3) = ((6 + 2) + 1)
8 df-9 12230 . . 3 9 = (8 + 1)
9 6p2e8 12319 . . . 4 (6 + 2) = 8
109oveq1i 7372 . . 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 1542  (class class class)co 7362  1c1 11059   + caddc 11061  2c2 12215  3c3 12216  6c6 12219  8c8 12221  9c9 12222
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2708  ax-1cn 11116  ax-addcl 11118  ax-addass 11123
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-rab 3411  df-v 3450  df-dif 3918  df-un 3920  df-in 3922  df-ss 3932  df-nul 4288  df-if 4492  df-sn 4592  df-pr 4594  df-op 4598  df-uni 4871  df-br 5111  df-iota 6453  df-fv 6509  df-ov 7365  df-2 12223  df-3 12224  df-4 12225  df-5 12226  df-6 12227  df-7 12228  df-8 12229  df-9 12230
This theorem is referenced by:  3t3e9  12327  6p4e10  12697  2exp8  16968  139prm  17003  2503lem2  17017  4001lem1  17020  4001lem2  17021  4001lem4  17023  log2ublem3  26314  ex-gcd  29443  hgt750lem2  33305  kur14lem8  33847  problem5  34297  fmtno5lem1  45819  139prmALT  45862  gboge9  46030  gbpart9  46035  nnsum4primeseven  46066
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