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Theorem 5p4e9 9098
Description: 5 + 4 = 9. (Contributed by NM, 11-May-2004.)
Assertion
Ref Expression
5p4e9  |-  ( 5  +  4 )  =  9

Proof of Theorem 5p4e9
StepHypRef Expression
1 df-4 9011 . . . 4  |-  4  =  ( 3  +  1 )
21oveq2i 5908 . . 3  |-  ( 5  +  4 )  =  ( 5  +  ( 3  +  1 ) )
3 5cn 9030 . . . 4  |-  5  e.  CC
4 3cn 9025 . . . 4  |-  3  e.  CC
5 ax-1cn 7935 . . . 4  |-  1  e.  CC
63, 4, 5addassi 7996 . . 3  |-  ( ( 5  +  3 )  +  1 )  =  ( 5  +  ( 3  +  1 ) )
72, 6eqtr4i 2213 . 2  |-  ( 5  +  4 )  =  ( ( 5  +  3 )  +  1 )
8 df-9 9016 . . 3  |-  9  =  ( 8  +  1 )
9 5p3e8 9097 . . . 4  |-  ( 5  +  3 )  =  8
109oveq1i 5907 . . 3  |-  ( ( 5  +  3 )  +  1 )  =  ( 8  +  1 )
118, 10eqtr4i 2213 . 2  |-  9  =  ( ( 5  +  3 )  +  1 )
127, 11eqtr4i 2213 1  |-  ( 5  +  4 )  =  9
Colors of variables: wff set class
Syntax hints:    = wceq 1364  (class class class)co 5897   1c1 7843    + caddc 7845   3c3 9002   4c4 9003   5c5 9004   8c8 9007   9c9 9008
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171  ax-resscn 7934  ax-1cn 7935  ax-1re 7936  ax-addrcl 7939  ax-addass 7944
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-rex 2474  df-v 2754  df-un 3148  df-in 3150  df-ss 3157  df-sn 3613  df-pr 3614  df-op 3616  df-uni 3825  df-br 4019  df-iota 5196  df-fv 5243  df-ov 5900  df-2 9009  df-3 9010  df-4 9011  df-5 9012  df-6 9013  df-7 9014  df-8 9015  df-9 9016
This theorem is referenced by:  5p5e10  9485
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