MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  6p3e9 Structured version   Visualization version   GIF version

Theorem 6p3e9 12424
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 12328 . . . 4 3 = (2 + 1)
21oveq2i 7442 . . 3 (6 + 3) = (6 + (2 + 1))
3 6cn 12355 . . . 4 6 ∈ ℂ
4 2cn 12339 . . . 4 2 ∈ ℂ
5 ax-1cn 11211 . . . 4 1 ∈ ℂ
63, 4, 5addassi 11269 . . 3 ((6 + 2) + 1) = (6 + (2 + 1))
72, 6eqtr4i 2766 . 2 (6 + 3) = ((6 + 2) + 1)
8 df-9 12334 . . 3 9 = (8 + 1)
9 6p2e8 12423 . . . 4 (6 + 2) = 8
109oveq1i 7441 . . 3 ((6 + 2) + 1) = (8 + 1)
118, 10eqtr4i 2766 . 2 9 = ((6 + 2) + 1)
127, 11eqtr4i 2766 1 (6 + 3) = 9
Colors of variables: wff setvar class
Syntax hints:   = wceq 1537  (class class class)co 7431  1c1 11154   + caddc 11156  2c2 12319  3c3 12320  6c6 12323  8c8 12325  9c9 12326
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706  ax-1cn 11211  ax-addcl 11213  ax-addass 11218
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-rab 3434  df-v 3480  df-dif 3966  df-un 3968  df-ss 3980  df-nul 4340  df-if 4532  df-sn 4632  df-pr 4634  df-op 4638  df-uni 4913  df-br 5149  df-iota 6516  df-fv 6571  df-ov 7434  df-2 12327  df-3 12328  df-4 12329  df-5 12330  df-6 12331  df-7 12332  df-8 12333  df-9 12334
This theorem is referenced by:  3t3e9  12431  6p4e10  12803  2exp8  17123  139prm  17158  2503lem2  17172  4001lem1  17175  4001lem2  17176  4001lem4  17178  log2ublem3  27006  ex-gcd  30486  hgt750lem2  34646  kur14lem8  35198  problem5  35654  fmtno5lem1  47478  139prmALT  47521  gboge9  47689  gbpart9  47694  nnsum4primeseven  47725
  Copyright terms: Public domain W3C validator