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Theorem 6p3e9 8319
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 8236 . . . 4  |-  3  =  ( 2  +  1 )
21oveq2i 5575 . . 3  |-  ( 6  +  3 )  =  ( 6  +  ( 2  +  1 ) )
3 6cn 8258 . . . 4  |-  6  e.  CC
4 2cn 8247 . . . 4  |-  2  e.  CC
5 ax-1cn 7201 . . . 4  |-  1  e.  CC
63, 4, 5addassi 7259 . . 3  |-  ( ( 6  +  2 )  +  1 )  =  ( 6  +  ( 2  +  1 ) )
72, 6eqtr4i 2106 . 2  |-  ( 6  +  3 )  =  ( ( 6  +  2 )  +  1 )
8 df-9 8242 . . 3  |-  9  =  ( 8  +  1 )
9 6p2e8 8318 . . . 4  |-  ( 6  +  2 )  =  8
109oveq1i 5574 . . 3  |-  ( ( 6  +  2 )  +  1 )  =  ( 8  +  1 )
118, 10eqtr4i 2106 . 2  |-  9  =  ( ( 6  +  2 )  +  1 )
127, 11eqtr4i 2106 1  |-  ( 6  +  3 )  =  9
Colors of variables: wff set class
Syntax hints:    = wceq 1285  (class class class)co 5564   1c1 7114    + caddc 7116   2c2 8226   3c3 8227   6c6 8230   8c8 8232   9c9 8233
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065  ax-resscn 7200  ax-1cn 7201  ax-1re 7202  ax-addrcl 7205  ax-addass 7210
This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-rex 2359  df-v 2612  df-un 2986  df-in 2988  df-ss 2995  df-sn 3422  df-pr 3423  df-op 3425  df-uni 3622  df-br 3806  df-iota 4917  df-fv 4960  df-ov 5567  df-2 8235  df-3 8236  df-4 8237  df-5 8238  df-6 8239  df-7 8240  df-8 8241  df-9 8242
This theorem is referenced by:  3t3e9  8326  6p4e10  8699  ex-gcd  10846
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