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Theorem 6p3e9 8821
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 8737 . . . 4  |-  3  =  ( 2  +  1 )
21oveq2i 5751 . . 3  |-  ( 6  +  3 )  =  ( 6  +  ( 2  +  1 ) )
3 6cn 8759 . . . 4  |-  6  e.  CC
4 2cn 8748 . . . 4  |-  2  e.  CC
5 ax-1cn 7677 . . . 4  |-  1  e.  CC
63, 4, 5addassi 7738 . . 3  |-  ( ( 6  +  2 )  +  1 )  =  ( 6  +  ( 2  +  1 ) )
72, 6eqtr4i 2139 . 2  |-  ( 6  +  3 )  =  ( ( 6  +  2 )  +  1 )
8 df-9 8743 . . 3  |-  9  =  ( 8  +  1 )
9 6p2e8 8820 . . . 4  |-  ( 6  +  2 )  =  8
109oveq1i 5750 . . 3  |-  ( ( 6  +  2 )  +  1 )  =  ( 8  +  1 )
118, 10eqtr4i 2139 . 2  |-  9  =  ( ( 6  +  2 )  +  1 )
127, 11eqtr4i 2139 1  |-  ( 6  +  3 )  =  9
Colors of variables: wff set class
Syntax hints:    = wceq 1314  (class class class)co 5740   1c1 7585    + caddc 7587   2c2 8728   3c3 8729   6c6 8732   8c8 8734   9c9 8735
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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097  ax-resscn 7676  ax-1cn 7677  ax-1re 7678  ax-addrcl 7681  ax-addass 7686
This theorem depends on definitions:  df-bi 116  df-3an 947  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-rex 2397  df-v 2660  df-un 3043  df-in 3045  df-ss 3052  df-sn 3501  df-pr 3502  df-op 3504  df-uni 3705  df-br 3898  df-iota 5056  df-fv 5099  df-ov 5743  df-2 8736  df-3 8737  df-4 8738  df-5 8739  df-6 8740  df-7 8741  df-8 8742  df-9 8743
This theorem is referenced by:  3t3e9  8828  6p4e10  9204  ex-gcd  12754
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