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Theorem 5p4e9 12425
Description: 5 + 4 = 9. (Contributed by NM, 11-May-2004.)
Assertion
Ref Expression
5p4e9 (5 + 4) = 9

Proof of Theorem 5p4e9
StepHypRef Expression
1 df-4 12332 . . . 4 4 = (3 + 1)
21oveq2i 7443 . . 3 (5 + 4) = (5 + (3 + 1))
3 5cn 12355 . . . 4 5 ∈ ℂ
4 3cn 12348 . . . 4 3 ∈ ℂ
5 ax-1cn 11214 . . . 4 1 ∈ ℂ
63, 4, 5addassi 11272 . . 3 ((5 + 3) + 1) = (5 + (3 + 1))
72, 6eqtr4i 2767 . 2 (5 + 4) = ((5 + 3) + 1)
8 df-9 12337 . . 3 9 = (8 + 1)
9 5p3e8 12424 . . . 4 (5 + 3) = 8
109oveq1i 7442 . . 3 ((5 + 3) + 1) = (8 + 1)
118, 10eqtr4i 2767 . 2 9 = ((5 + 3) + 1)
127, 11eqtr4i 2767 1 (5 + 4) = 9
Colors of variables: wff setvar class
Syntax hints:   = wceq 1539  (class class class)co 7432  1c1 11157   + caddc 11159  3c3 12323  4c4 12324  5c5 12325  8c8 12328  9c9 12329
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707  ax-1cn 11214  ax-addcl 11216  ax-addass 11221
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1542  df-fal 1552  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-rab 3436  df-v 3481  df-dif 3953  df-un 3955  df-ss 3967  df-nul 4333  df-if 4525  df-sn 4626  df-pr 4628  df-op 4632  df-uni 4907  df-br 5143  df-iota 6513  df-fv 6568  df-ov 7435  df-2 12330  df-3 12331  df-4 12332  df-5 12333  df-6 12334  df-7 12335  df-8 12336  df-9 12337
This theorem is referenced by:  5p5e10  12806  139prm  17162  1259lem3  17171  1259lem4  17172  2503lem2  17176  4001lem1  17179  4001lem2  17180  hgt750lem2  34668  problem1  35671  problem2  35672  resqrtvalex  43663  imsqrtvalex  43664  inductionexd  44173  139prmALT  47588
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