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Theorem 6p2e8 8862
Description: 6 + 2 = 8. (Contributed by NM, 11-May-2004.)
Assertion
Ref Expression
6p2e8 (6 + 2) = 8

Proof of Theorem 6p2e8
StepHypRef Expression
1 df-2 8772 . . . . 5 2 = (1 + 1)
21oveq2i 5778 . . . 4 (6 + 2) = (6 + (1 + 1))
3 6cn 8795 . . . . 5 6 ∈ ℂ
4 ax-1cn 7706 . . . . 5 1 ∈ ℂ
53, 4, 4addassi 7767 . . . 4 ((6 + 1) + 1) = (6 + (1 + 1))
62, 5eqtr4i 2161 . . 3 (6 + 2) = ((6 + 1) + 1)
7 df-7 8777 . . . 4 7 = (6 + 1)
87oveq1i 5777 . . 3 (7 + 1) = ((6 + 1) + 1)
96, 8eqtr4i 2161 . 2 (6 + 2) = (7 + 1)
10 df-8 8778 . 2 8 = (7 + 1)
119, 10eqtr4i 2161 1 (6 + 2) = 8
Colors of variables: wff set class
Syntax hints:   = wceq 1331  (class class class)co 5767  1c1 7614   + caddc 7616  2c2 8764  6c6 8768  7c7 8769  8c8 8770
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119  ax-resscn 7705  ax-1cn 7706  ax-1re 7707  ax-addrcl 7710  ax-addass 7715
This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-rex 2420  df-v 2683  df-un 3070  df-in 3072  df-ss 3079  df-sn 3528  df-pr 3529  df-op 3531  df-uni 3732  df-br 3925  df-iota 5083  df-fv 5126  df-ov 5770  df-2 8772  df-3 8773  df-4 8774  df-5 8775  df-6 8776  df-7 8777  df-8 8778
This theorem is referenced by:  6p3e9  8863  6t3e18  9279
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