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Theorem 5p4e9 8720
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 8639 . . . 4  |-  4  =  ( 3  +  1 )
21oveq2i 5717 . . 3  |-  ( 5  +  4 )  =  ( 5  +  ( 3  +  1 ) )
3 5cn 8658 . . . 4  |-  5  e.  CC
4 3cn 8653 . . . 4  |-  3  e.  CC
5 ax-1cn 7588 . . . 4  |-  1  e.  CC
63, 4, 5addassi 7646 . . 3  |-  ( ( 5  +  3 )  +  1 )  =  ( 5  +  ( 3  +  1 ) )
72, 6eqtr4i 2123 . 2  |-  ( 5  +  4 )  =  ( ( 5  +  3 )  +  1 )
8 df-9 8644 . . 3  |-  9  =  ( 8  +  1 )
9 5p3e8 8719 . . . 4  |-  ( 5  +  3 )  =  8
109oveq1i 5716 . . 3  |-  ( ( 5  +  3 )  +  1 )  =  ( 8  +  1 )
118, 10eqtr4i 2123 . 2  |-  9  =  ( ( 5  +  3 )  +  1 )
127, 11eqtr4i 2123 1  |-  ( 5  +  4 )  =  9
Colors of variables: wff set class
Syntax hints:    = wceq 1299  (class class class)co 5706   1c1 7501    + caddc 7503   3c3 8630   4c4 8631   5c5 8632   8c8 8635   9c9 8636
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082  ax-resscn 7587  ax-1cn 7588  ax-1re 7589  ax-addrcl 7592  ax-addass 7597
This theorem depends on definitions:  df-bi 116  df-3an 932  df-tru 1302  df-nf 1405  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-nfc 2229  df-rex 2381  df-v 2643  df-un 3025  df-in 3027  df-ss 3034  df-sn 3480  df-pr 3481  df-op 3483  df-uni 3684  df-br 3876  df-iota 5024  df-fv 5067  df-ov 5709  df-2 8637  df-3 8638  df-4 8639  df-5 8640  df-6 8641  df-7 8642  df-8 8643  df-9 8644
This theorem is referenced by:  5p5e10  9104
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