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Theorem 7p2e9 8250
Description: 7 + 2 = 9. (Contributed by NM, 11-May-2004.)
Assertion
Ref Expression
7p2e9  |-  ( 7  +  2 )  =  9

Proof of Theorem 7p2e9
StepHypRef Expression
1 df-2 8165 . . . . 5  |-  2  =  ( 1  +  1 )
21oveq2i 5554 . . . 4  |-  ( 7  +  2 )  =  ( 7  +  ( 1  +  1 ) )
3 7cn 8190 . . . . 5  |-  7  e.  CC
4 ax-1cn 7131 . . . . 5  |-  1  e.  CC
53, 4, 4addassi 7189 . . . 4  |-  ( ( 7  +  1 )  +  1 )  =  ( 7  +  ( 1  +  1 ) )
62, 5eqtr4i 2105 . . 3  |-  ( 7  +  2 )  =  ( ( 7  +  1 )  +  1 )
7 df-8 8171 . . . 4  |-  8  =  ( 7  +  1 )
87oveq1i 5553 . . 3  |-  ( 8  +  1 )  =  ( ( 7  +  1 )  +  1 )
96, 8eqtr4i 2105 . 2  |-  ( 7  +  2 )  =  ( 8  +  1 )
10 df-9 8172 . 2  |-  9  =  ( 8  +  1 )
119, 10eqtr4i 2105 1  |-  ( 7  +  2 )  =  9
Colors of variables: wff set class
Syntax hints:    = wceq 1285  (class class class)co 5543   1c1 7044    + caddc 7046   2c2 8156   7c7 8161   8c8 8162   9c9 8163
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 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-resscn 7130  ax-1cn 7131  ax-1re 7132  ax-addrcl 7135  ax-addass 7140
This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-rex 2355  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-sn 3412  df-pr 3413  df-op 3415  df-uni 3610  df-br 3794  df-iota 4897  df-fv 4940  df-ov 5546  df-2 8165  df-3 8166  df-4 8167  df-5 8168  df-6 8169  df-7 8170  df-8 8171  df-9 8172
This theorem is referenced by:  7p3e10  8632  7t7e49  8671
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