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Theorem 5p4e9 8501
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 8421 . . . 4  |-  4  =  ( 3  +  1 )
21oveq2i 5626 . . 3  |-  ( 5  +  4 )  =  ( 5  +  ( 3  +  1 ) )
3 5cn 8440 . . . 4  |-  5  e.  CC
4 3cn 8435 . . . 4  |-  3  e.  CC
5 ax-1cn 7385 . . . 4  |-  1  e.  CC
63, 4, 5addassi 7443 . . 3  |-  ( ( 5  +  3 )  +  1 )  =  ( 5  +  ( 3  +  1 ) )
72, 6eqtr4i 2108 . 2  |-  ( 5  +  4 )  =  ( ( 5  +  3 )  +  1 )
8 df-9 8426 . . 3  |-  9  =  ( 8  +  1 )
9 5p3e8 8500 . . . 4  |-  ( 5  +  3 )  =  8
109oveq1i 5625 . . 3  |-  ( ( 5  +  3 )  +  1 )  =  ( 8  +  1 )
118, 10eqtr4i 2108 . 2  |-  9  =  ( ( 5  +  3 )  +  1 )
127, 11eqtr4i 2108 1  |-  ( 5  +  4 )  =  9
Colors of variables: wff set class
Syntax hints:    = wceq 1287  (class class class)co 5615   1c1 7298    + caddc 7300   3c3 8411   4c4 8412   5c5 8413   8c8 8416   9c9 8417
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 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067  ax-resscn 7384  ax-1cn 7385  ax-1re 7386  ax-addrcl 7389  ax-addass 7394
This theorem depends on definitions:  df-bi 115  df-3an 924  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-rex 2361  df-v 2617  df-un 2992  df-in 2994  df-ss 3001  df-sn 3437  df-pr 3438  df-op 3440  df-uni 3639  df-br 3823  df-iota 4948  df-fv 4991  df-ov 5618  df-2 8419  df-3 8420  df-4 8421  df-5 8422  df-6 8423  df-7 8424  df-8 8425  df-9 8426
This theorem is referenced by:  5p5e10  8882
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