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Theorem 6p2e8 8982
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 8892 . . . . 5  |-  2  =  ( 1  +  1 )
21oveq2i 5835 . . . 4  |-  ( 6  +  2 )  =  ( 6  +  ( 1  +  1 ) )
3 6cn 8915 . . . . 5  |-  6  e.  CC
4 ax-1cn 7825 . . . . 5  |-  1  e.  CC
53, 4, 4addassi 7886 . . . 4  |-  ( ( 6  +  1 )  +  1 )  =  ( 6  +  ( 1  +  1 ) )
62, 5eqtr4i 2181 . . 3  |-  ( 6  +  2 )  =  ( ( 6  +  1 )  +  1 )
7 df-7 8897 . . . 4  |-  7  =  ( 6  +  1 )
87oveq1i 5834 . . 3  |-  ( 7  +  1 )  =  ( ( 6  +  1 )  +  1 )
96, 8eqtr4i 2181 . 2  |-  ( 6  +  2 )  =  ( 7  +  1 )
10 df-8 8898 . 2  |-  8  =  ( 7  +  1 )
119, 10eqtr4i 2181 1  |-  ( 6  +  2 )  =  8
Colors of variables: wff set class
Syntax hints:    = wceq 1335  (class class class)co 5824   1c1 7733    + caddc 7735   2c2 8884   6c6 8888   7c7 8889   8c8 8890
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 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139  ax-resscn 7824  ax-1cn 7825  ax-1re 7826  ax-addrcl 7829  ax-addass 7834
This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-rex 2441  df-v 2714  df-un 3106  df-in 3108  df-ss 3115  df-sn 3566  df-pr 3567  df-op 3569  df-uni 3773  df-br 3966  df-iota 5135  df-fv 5178  df-ov 5827  df-2 8892  df-3 8893  df-4 8894  df-5 8895  df-6 8896  df-7 8897  df-8 8898
This theorem is referenced by:  6p3e9  8983  6t3e18  9399
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