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Theorem 6p3e9 11789
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 11693 . . . 4 3 = (2 + 1)
21oveq2i 7150 . . 3 (6 + 3) = (6 + (2 + 1))
3 6cn 11720 . . . 4 6 ∈ ℂ
4 2cn 11704 . . . 4 2 ∈ ℂ
5 ax-1cn 10588 . . . 4 1 ∈ ℂ
63, 4, 5addassi 10644 . . 3 ((6 + 2) + 1) = (6 + (2 + 1))
72, 6eqtr4i 2827 . 2 (6 + 3) = ((6 + 2) + 1)
8 df-9 11699 . . 3 9 = (8 + 1)
9 6p2e8 11788 . . . 4 (6 + 2) = 8
109oveq1i 7149 . . 3 ((6 + 2) + 1) = (8 + 1)
118, 10eqtr4i 2827 . 2 9 = ((6 + 2) + 1)
127, 11eqtr4i 2827 1 (6 + 3) = 9
Colors of variables: wff setvar class
Syntax hints:   = wceq 1538  (class class class)co 7139  1c1 10531   + caddc 10533  2c2 11684  3c3 11685  6c6 11688  8c8 11690  9c9 11691
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 1911  ax-6 1970  ax-7 2015  ax-8 2114  ax-9 2122  ax-ext 2773  ax-1cn 10588  ax-addcl 10590  ax-addass 10595
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-ex 1782  df-sb 2070  df-clab 2780  df-cleq 2794  df-clel 2873  df-v 3446  df-un 3889  df-in 3891  df-ss 3901  df-sn 4529  df-pr 4531  df-op 4535  df-uni 4804  df-br 5034  df-iota 6287  df-fv 6336  df-ov 7142  df-2 11692  df-3 11693  df-4 11694  df-5 11695  df-6 11696  df-7 11697  df-8 11698  df-9 11699
This theorem is referenced by:  3t3e9  11796  6p4e10  12162  2exp8  16418  139prm  16452  2503lem2  16466  4001lem1  16469  4001lem2  16470  4001lem4  16472  log2ublem3  25537  ex-gcd  28245  hgt750lem2  32031  kur14lem8  32568  problem5  33020  fmtno5lem1  44057  139prmALT  44100  gboge9  44269  gbpart9  44274  nnsum4primeseven  44305
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