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Theorem 5p3e8 12423
Description: 5 + 3 = 8. (Contributed by NM, 11-May-2004.)
Assertion
Ref Expression
5p3e8 (5 + 3) = 8

Proof of Theorem 5p3e8
StepHypRef Expression
1 df-3 12330 . . . 4 3 = (2 + 1)
21oveq2i 7442 . . 3 (5 + 3) = (5 + (2 + 1))
3 5cn 12354 . . . 4 5 ∈ ℂ
4 2cn 12341 . . . 4 2 ∈ ℂ
5 ax-1cn 11213 . . . 4 1 ∈ ℂ
63, 4, 5addassi 11271 . . 3 ((5 + 2) + 1) = (5 + (2 + 1))
72, 6eqtr4i 2768 . 2 (5 + 3) = ((5 + 2) + 1)
8 df-8 12335 . . 3 8 = (7 + 1)
9 5p2e7 12422 . . . 4 (5 + 2) = 7
109oveq1i 7441 . . 3 ((5 + 2) + 1) = (7 + 1)
118, 10eqtr4i 2768 . 2 8 = ((5 + 2) + 1)
127, 11eqtr4i 2768 1 (5 + 3) = 8
Colors of variables: wff setvar class
Syntax hints:   = wceq 1540  (class class class)co 7431  1c1 11156   + caddc 11158  2c2 12321  3c3 12322  5c5 12324  7c7 12326  8c8 12327
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708  ax-1cn 11213  ax-addcl 11215  ax-addass 11220
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-rab 3437  df-v 3482  df-dif 3954  df-un 3956  df-ss 3968  df-nul 4334  df-if 4526  df-sn 4627  df-pr 4629  df-op 4633  df-uni 4908  df-br 5144  df-iota 6514  df-fv 6569  df-ov 7434  df-2 12329  df-3 12330  df-4 12331  df-5 12332  df-6 12333  df-7 12334  df-8 12335
This theorem is referenced by:  5p4e9  12424  ef01bndlem  16220  2exp16  17128  1259lem2  17169  log2ublem3  26991  log2ub  26992  bposlem8  27335  lgsdir2lem1  27369  fib6  34408  235t711  42339  ex-decpmul  42340  fmtno5lem2  47541  fmtno5lem4  47543  257prm  47548  gbpart8  47755  8gbe  47760  evengpop3  47785  ackval3012  48613
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