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Theorem 4p4e8 12421
Description: 4 + 4 = 8. (Contributed by NM, 11-May-2004.)
Assertion
Ref Expression
4p4e8 (4 + 4) = 8

Proof of Theorem 4p4e8
StepHypRef Expression
1 df-4 12331 . . . 4 4 = (3 + 1)
21oveq2i 7442 . . 3 (4 + 4) = (4 + (3 + 1))
3 4cn 12351 . . . 4 4 ∈ ℂ
4 3cn 12347 . . . 4 3 ∈ ℂ
5 ax-1cn 11213 . . . 4 1 ∈ ℂ
63, 4, 5addassi 11271 . . 3 ((4 + 3) + 1) = (4 + (3 + 1))
72, 6eqtr4i 2768 . 2 (4 + 4) = ((4 + 3) + 1)
8 df-8 12335 . . 3 8 = (7 + 1)
9 4p3e7 12420 . . . 4 (4 + 3) = 7
109oveq1i 7441 . . 3 ((4 + 3) + 1) = (7 + 1)
118, 10eqtr4i 2768 . 2 8 = ((4 + 3) + 1)
127, 11eqtr4i 2768 1 (4 + 4) = 8
Colors of variables: wff setvar class
Syntax hints:   = wceq 1540  (class class class)co 7431  1c1 11156   + caddc 11158  3c3 12322  4c4 12323  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:  4t2e8  12434  83prm  17160  1259lem2  17169  1259lem3  17170  2503lem2  17175  4001lem2  17179  quart1lem  26898  log2ub  26992  hgt750lem2  34667  3exp7  42054  3lexlogpow5ineq1  42055  3cubeslem3r  42698
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