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Theorem 6p2e8 9027
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 8937 . . . . 5  |-  2  =  ( 1  +  1 )
21oveq2i 5864 . . . 4  |-  ( 6  +  2 )  =  ( 6  +  ( 1  +  1 ) )
3 6cn 8960 . . . . 5  |-  6  e.  CC
4 ax-1cn 7867 . . . . 5  |-  1  e.  CC
53, 4, 4addassi 7928 . . . 4  |-  ( ( 6  +  1 )  +  1 )  =  ( 6  +  ( 1  +  1 ) )
62, 5eqtr4i 2194 . . 3  |-  ( 6  +  2 )  =  ( ( 6  +  1 )  +  1 )
7 df-7 8942 . . . 4  |-  7  =  ( 6  +  1 )
87oveq1i 5863 . . 3  |-  ( 7  +  1 )  =  ( ( 6  +  1 )  +  1 )
96, 8eqtr4i 2194 . 2  |-  ( 6  +  2 )  =  ( 7  +  1 )
10 df-8 8943 . 2  |-  8  =  ( 7  +  1 )
119, 10eqtr4i 2194 1  |-  ( 6  +  2 )  =  8
Colors of variables: wff set class
Syntax hints:    = wceq 1348  (class class class)co 5853   1c1 7775    + caddc 7777   2c2 8929   6c6 8933   7c7 8934   8c8 8935
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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152  ax-resscn 7866  ax-1cn 7867  ax-1re 7868  ax-addrcl 7871  ax-addass 7876
This theorem depends on definitions:  df-bi 116  df-3an 975  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-rex 2454  df-v 2732  df-un 3125  df-in 3127  df-ss 3134  df-sn 3589  df-pr 3590  df-op 3592  df-uni 3797  df-br 3990  df-iota 5160  df-fv 5206  df-ov 5856  df-2 8937  df-3 8938  df-4 8939  df-5 8940  df-6 8941  df-7 8942  df-8 8943
This theorem is referenced by:  6p3e9  9028  6t3e18  9447
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