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Theorem 6p3e9 12309
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 12213 . . . 4 3 = (2 + 1)
21oveq2i 7364 . . 3 (6 + 3) = (6 + (2 + 1))
3 6cn 12240 . . . 4 6 ∈ ℂ
4 2cn 12224 . . . 4 2 ∈ ℂ
5 ax-1cn 11105 . . . 4 1 ∈ ℂ
63, 4, 5addassi 11161 . . 3 ((6 + 2) + 1) = (6 + (2 + 1))
72, 6eqtr4i 2767 . 2 (6 + 3) = ((6 + 2) + 1)
8 df-9 12219 . . 3 9 = (8 + 1)
9 6p2e8 12308 . . . 4 (6 + 2) = 8
109oveq1i 7363 . . 3 ((6 + 2) + 1) = (8 + 1)
118, 10eqtr4i 2767 . 2 9 = ((6 + 2) + 1)
127, 11eqtr4i 2767 1 (6 + 3) = 9
Colors of variables: wff setvar class
Syntax hints:   = wceq 1541  (class class class)co 7353  1c1 11048   + caddc 11050  2c2 12204  3c3 12205  6c6 12208  8c8 12210  9c9 12211
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2707  ax-1cn 11105  ax-addcl 11107  ax-addass 11112
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-sb 2068  df-clab 2714  df-cleq 2728  df-clel 2814  df-rab 3406  df-v 3445  df-dif 3911  df-un 3913  df-in 3915  df-ss 3925  df-nul 4281  df-if 4485  df-sn 4585  df-pr 4587  df-op 4591  df-uni 4864  df-br 5104  df-iota 6445  df-fv 6501  df-ov 7356  df-2 12212  df-3 12213  df-4 12214  df-5 12215  df-6 12216  df-7 12217  df-8 12218  df-9 12219
This theorem is referenced by:  3t3e9  12316  6p4e10  12686  2exp8  16953  139prm  16988  2503lem2  17002  4001lem1  17005  4001lem2  17006  4001lem4  17008  log2ublem3  26282  ex-gcd  29287  hgt750lem2  33134  kur14lem8  33676  problem5  34126  fmtno5lem1  45677  139prmALT  45720  gboge9  45888  gbpart9  45893  nnsum4primeseven  45924
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