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Theorem 5p2e7 8129
Description: 5 + 2 = 7. (Contributed by NM, 11-May-2004.)
Assertion
Ref Expression
5p2e7  |-  ( 5  +  2 )  =  7

Proof of Theorem 5p2e7
StepHypRef Expression
1 df-2 8049 . . . . 5  |-  2  =  ( 1  +  1 )
21oveq2i 5551 . . . 4  |-  ( 5  +  2 )  =  ( 5  +  ( 1  +  1 ) )
3 5cn 8070 . . . . 5  |-  5  e.  CC
4 ax-1cn 7035 . . . . 5  |-  1  e.  CC
53, 4, 4addassi 7093 . . . 4  |-  ( ( 5  +  1 )  +  1 )  =  ( 5  +  ( 1  +  1 ) )
62, 5eqtr4i 2079 . . 3  |-  ( 5  +  2 )  =  ( ( 5  +  1 )  +  1 )
7 df-6 8053 . . . 4  |-  6  =  ( 5  +  1 )
87oveq1i 5550 . . 3  |-  ( 6  +  1 )  =  ( ( 5  +  1 )  +  1 )
96, 8eqtr4i 2079 . 2  |-  ( 5  +  2 )  =  ( 6  +  1 )
10 df-7 8054 . 2  |-  7  =  ( 6  +  1 )
119, 10eqtr4i 2079 1  |-  ( 5  +  2 )  =  7
Colors of variables: wff set class
Syntax hints:    = wceq 1259  (class class class)co 5540   1c1 6948    + caddc 6950   2c2 8040   5c5 8043   6c6 8044   7c7 8045
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-resscn 7034  ax-1cn 7035  ax-1re 7036  ax-addrcl 7039  ax-addass 7044
This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rex 2329  df-v 2576  df-un 2950  df-in 2952  df-ss 2959  df-sn 3409  df-pr 3410  df-op 3412  df-uni 3609  df-br 3793  df-iota 4895  df-fv 4938  df-ov 5543  df-2 8049  df-3 8050  df-4 8051  df-5 8052  df-6 8053  df-7 8054
This theorem is referenced by:  5p3e8  8130
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