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Theorem 5p4e9 8836
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 8749 . . . 4  |-  4  =  ( 3  +  1 )
21oveq2i 5753 . . 3  |-  ( 5  +  4 )  =  ( 5  +  ( 3  +  1 ) )
3 5cn 8768 . . . 4  |-  5  e.  CC
4 3cn 8763 . . . 4  |-  3  e.  CC
5 ax-1cn 7681 . . . 4  |-  1  e.  CC
63, 4, 5addassi 7742 . . 3  |-  ( ( 5  +  3 )  +  1 )  =  ( 5  +  ( 3  +  1 ) )
72, 6eqtr4i 2141 . 2  |-  ( 5  +  4 )  =  ( ( 5  +  3 )  +  1 )
8 df-9 8754 . . 3  |-  9  =  ( 8  +  1 )
9 5p3e8 8835 . . . 4  |-  ( 5  +  3 )  =  8
109oveq1i 5752 . . 3  |-  ( ( 5  +  3 )  +  1 )  =  ( 8  +  1 )
118, 10eqtr4i 2141 . 2  |-  9  =  ( ( 5  +  3 )  +  1 )
127, 11eqtr4i 2141 1  |-  ( 5  +  4 )  =  9
Colors of variables: wff set class
Syntax hints:    = wceq 1316  (class class class)co 5742   1c1 7589    + caddc 7591   3c3 8740   4c4 8741   5c5 8742   8c8 8745   9c9 8746
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099  ax-resscn 7680  ax-1cn 7681  ax-1re 7682  ax-addrcl 7685  ax-addass 7690
This theorem depends on definitions:  df-bi 116  df-3an 949  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-rex 2399  df-v 2662  df-un 3045  df-in 3047  df-ss 3054  df-sn 3503  df-pr 3504  df-op 3506  df-uni 3707  df-br 3900  df-iota 5058  df-fv 5101  df-ov 5745  df-2 8747  df-3 8748  df-4 8749  df-5 8750  df-6 8751  df-7 8752  df-8 8753  df-9 8754
This theorem is referenced by:  5p5e10  9220
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