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Theorem 6p3e9 9028
Description: 6 + 3 = 9. (Contributed by NM, 11-May-2004.)
Assertion
Ref Expression
6p3e9  |-  ( 6  +  3 )  =  9

Proof of Theorem 6p3e9
StepHypRef Expression
1 df-3 8938 . . . 4  |-  3  =  ( 2  +  1 )
21oveq2i 5864 . . 3  |-  ( 6  +  3 )  =  ( 6  +  ( 2  +  1 ) )
3 6cn 8960 . . . 4  |-  6  e.  CC
4 2cn 8949 . . . 4  |-  2  e.  CC
5 ax-1cn 7867 . . . 4  |-  1  e.  CC
63, 4, 5addassi 7928 . . 3  |-  ( ( 6  +  2 )  +  1 )  =  ( 6  +  ( 2  +  1 ) )
72, 6eqtr4i 2194 . 2  |-  ( 6  +  3 )  =  ( ( 6  +  2 )  +  1 )
8 df-9 8944 . . 3  |-  9  =  ( 8  +  1 )
9 6p2e8 9027 . . . 4  |-  ( 6  +  2 )  =  8
109oveq1i 5863 . . 3  |-  ( ( 6  +  2 )  +  1 )  =  ( 8  +  1 )
118, 10eqtr4i 2194 . 2  |-  9  =  ( ( 6  +  2 )  +  1 )
127, 11eqtr4i 2194 1  |-  ( 6  +  3 )  =  9
Colors of variables: wff set class
Syntax hints:    = wceq 1348  (class class class)co 5853   1c1 7775    + caddc 7777   2c2 8929   3c3 8930   6c6 8933   8c8 8935   9c9 8936
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  df-9 8944
This theorem is referenced by:  3t3e9  9035  6p4e10  9414  ex-gcd  13766
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